;152m)[?7h[?12l[?25h[?25l[?7l^(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l-)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l1)(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(0)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(1)

[?7h[?12l[?25h[?2004l[?7h1/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(2)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l2)*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-2)*(C.x)^(-2)*C.dx).jth_component(0)

[?7h[?12l[?25h[?2004l[?7h1/(x^5 + 2*x^3)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-2)*(C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l12[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lx2C.d.jth_componen(0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.coordinates()[?7h[?12l[?25h[?25l[?7l = C.e_rham_basis()[0][?7h[?12l[?25h[?25l[?7lC.de_rham_bsis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.x).jth_component(2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8((C.x)^(-2)*C.dx)

[?7h[?12l[?25h[?2004lcomponent, q, r 1/x^2 0 1
component, q, r 0 0 0
[?7h(0 dx, ((-1)/x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004laux.h2, decomposition_g0_g8(aux.h2, prec=prec) ((x^4 + x^2 + 1)/x^3)*y (x*y, 2/x^3*y, 1/x*y) ((x^4 + 1)/x^3)*y
aux.h2, decomposition_g0_g8(aux.h2, prec=prec) (x^6/(x^2 + 2))*y ((x^6/(x^2 + 2))*y, 0, 0) (x^6/(x^2 + 2))*y
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:66, in coordinates(self)

KeyError: (1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.coordinates()[?7h[?12l[?25h[?25l[?7lutm(b[0]) - 4*b[0]-6*b[1][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm(b[0]) - 4*b[0]-6*b[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6*b[1][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: autom(b[0]) - 4*b[0]-6*b[0]

[?7h[?12l[?25h[?2004l[?7h(V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
(0, 1)
aux.h2, decomposition_g0_g8(aux.h2, prec=prec) ((x^4 + x^2 + 1)/x^3)*y (x*y, 2/x^3*y, 1/x*y) ((x^4 + 1)/x^3)*y
(0, x)
(0, 2/x)
aux.h2, decomposition_g0_g8(aux.h2, prec=prec) (x^6/(x^2 + 2))*y ((x^6/(x^2 + 2))*y, 0, 0) (x^6/(x^2 + 2))*y
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Input In [87], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:66, in coordinates(self)

KeyError: (1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^3 - x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega0.frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7l8.frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^4 + 1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8.frobenius().valuation()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [90], in <cell line: 1>()
----> 1 b[Integer(0)].omega8.frobenius().valuation()

AttributeError: 'superelliptic_form' object has no attribute 'valuation'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8.frobenius().valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-6 + t^-2 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
t^2 + t^10 + O(t^12)
(0, x)
t^-4 + t^4 + O(t^6)
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Input In [92], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:66, in coordinates(self)

KeyError: (1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
t^2 + t^10 + O(t^12)
(0, x)
2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Input In [93], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:66, in coordinates(self)

KeyError: (1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-6 + t^-2 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
t^2 + t^10 + O(t^12)
aux (is h1 = 0?) V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
(0, x)
2*t^8 + 2*t^16 + O(t^18)
aux (is h1 = 0?) V(((-x^16 - x^14 - x^12 + x^10 - x^8 - x^6 + x^4 - x^2 - 1)/(x^8*y - x^6*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Input In [95], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:66, in coordinates(self)

KeyError: (1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
t^2 + t^10 + O(t^12)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [96], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:16, in <module>

File <string>:375, in crystalline_cohomology_basis(self, prec)

File <string>:363, in de_rham_witt_lift(cech_class, prec)

File <string>:18, in __eq__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
t^2 + t^10 + O(t^12)
(0, x)
2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0].omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) - 4*b[0]-6*b[0][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l(b[0]) - 4*b[0]-6*b[0][?7h[?12l[?25h[?25l[?7lsage: autom(b[0]) - 4*b[0]-6*b[0]

[?7h[?12l[?25h[?2004l[?7h(V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) - 4*b[0]-6*b[0][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(autom(b[0]) - 4*b[0]-6*b[0])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (autom(b[0]) - 4*b[0]-6*b[0]).reduce()

[?7h[?12l[?25h[?2004l[?7h(V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), [0], V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) - 4*b[0]-6*b[0][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l(b[0]) - 4*b[0]-6*b[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().reduce(), (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7lcoordinates(basis=b)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates(basis = b)[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).coordinates(basis = b)

[?7h[?12l[?25h[?2004l(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[?7h[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/(C.x^2*C.y + C.x*C.y)) C.dx[?7h[?12l[?25h[?25l[?7lsage: (C.one/(C.x^2*C.y + C.x*C.y)) C.dx

[?7h[?12l[?25h[?2004l  Input In [101]
    (C.one/(C.x**Integer(2)*C.y + C.x*C.y)) C.dx
                                            ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/(C.x^2*C.y + C.x*C.y)) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()( C.dx[?7h[?12l[?25h[?25l[?7l() C.dx[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.one/(C.x^2*C.y + C.x*C.y))* C.dx

[?7h[?12l[?25h[?2004l[?7h(1/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/(C.x^2*C.y + C.x*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.one/(C.x^2*C.y + C.x*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/(C.x^2*C.y + C.x*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l C.dx[?7h[?12l[?25h[?25l[?7lautm(b[0]).coordinates(basis= b)[?7h[?12l[?25h[?25l[?7l(C.ne/(C.x^2*C.y + C.x*C.y))C.dx[?7h[?12l[?25h[?25l[?7l* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.one/(C.x^2*C.y + C.x*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l(C.one/(C.x^2*C.y + C.x*C.y)* C.dx).cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^4 + 2*t^6 + t^8 + O(t^14)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[].omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lor()[?7h[?12l[?25h[?25l[?7lomr()[?7h[?12l[?25h[?25l[?7ler()[?7h[?12l[?25h[?25l[?7lgr()[?7h[?12l[?25h[?25l[?7lar()[?7h[?12l[?25h[?25l[?7l0r()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].omega0.r()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [107], in <cell line: 1>()
----> 1 b[Integer(0)].omega0.r()

AttributeError: 'superelliptic_drw_form' object has no attribute 'r'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega0.r()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lR()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].omega0.R()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [108], in <cell line: 1>()
----> 1 b[Integer(0)].omega0.R()

AttributeError: 'superelliptic_drw_form' object has no attribute 'R'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega0.R()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].omega0.R()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].omega0.r()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega0.r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lus()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega0.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega0.r()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l8.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8.r()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8.r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8.frobenius()

[?7h[?12l[?25h[?2004l[?7h(1/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8.frobenius()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + O(t^12)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l352%9[?7h[?12l[?25h[?25l[?7l*a[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: 3*b[0]

[?7h[?12l[?25h[?2004l[?7h(V((x/(x^2*y - y)) dx), [0], V((x/(x^2*y - y)) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates()

[?7h[?12l[?25h[?2004l(1, 0)
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
aux before reduce (0, [0], 0)
aux V(smth) (0, [0], 0)
aux.omega0.omega.cartier() 0 dx
[?7h[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lab[0].cordinates()[?7h[?12l[?25h[?25l[?7lub[0].cordinates()[?7h[?12l[?25h[?25l[?7ltb[0].cordinates()[?7h[?12l[?25h[?25l[?7lob[0].cordinates()[?7h[?12l[?25h[?25l[?7lmb[0].cordinates()[?7h[?12l[?25h[?25l[?7l(b[0].cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([]).cordinates()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).coordinates()

[?7h[?12l[?25h[?2004l(1, 0)
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[?7h[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/(C.x^2*C.y + C.x*C.y)) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.one/(C.x^2*C.y + C.x*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2/(x^2 + x))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*/(x^2 + x)*y[?7h[?12l[?25h[?25l[?7lC/(x^2 + x)*y[?7h[?12l[?25h[?25l[?7l./(x^2 + x)*y[?7h[?12l[?25h[?25l[?7lo/(x^2 + x)*y[?7h[?12l[?25h[?25l[?7ln/(x^2 + x)*y[?7h[?12l[?25h[?25l[?7le/(x^2 + x)*y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + x)*y[?7h[?12l[?25h[?25l[?7l.x^2 + x)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)*y[?7h[?12l[?25h[?25l[?7l.x)*y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (2*C.one/(C.x^2 + C.x))*C.y

[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7le(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lc(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lo(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lm(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lp(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lo(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7ls(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7li(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lt(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7li(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lo(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7ln(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l_(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7li(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7ln(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lt(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lo(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l_(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lg(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lo(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l_(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7lg(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l8(2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l((2*C.one/(C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_into_go_g8((2*C.one/(C.x^2 + C.x))*C.y)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [121], in <cell line: 1>()
----> 1 decomposition_into_go_g8((Integer(2)*C.one/(C.x**Integer(2) + C.x))*C.y)

NameError: name 'decomposition_into_go_g8' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_into_go_g8((2*C.one/(C.x^2 + C.x))*C.y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_g8(2*C.one/(C.x^2 + C.x)*C.y)[?7h[?12l[?25h[?25l[?7l0_g8(2*C.one/(C.x^2 + C.x)*C.y)[?7h[?12l[?25h[?25l[?7lsage: decomposition_into_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [122], in <cell line: 1>()
----> 1 decomposition_into_g0_g8((Integer(2)*C.one/(C.x**Integer(2) + C.x))*C.y)

NameError: name 'decomposition_into_g0_g8' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_into_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0_g8(2*C.one/(C.x^2 + C.x)*C.y)[?7h[?12l[?25h[?25l[?7lg0_g8(2*C.one/(C.x^2 + C.x)*C.y)[?7h[?12l[?25h[?25l[?7lg0_g8(2*C.one/(C.x^2 + C.x)*C.y)[?7h[?12l[?25h[?25l[?7lg0_g8(2*C.one/(C.x^2 + C.x)*C.y)[?7h[?12l[?25h[?25l[?7lg0_g8(2*C.one/(C.x^2 + C.x)*C.y)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)

[?7h[?12l[?25h[?2004l[?7h(0, (1/(x^2 + x))*y, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m "nieudane proby coordinates dla cech_drw"
[master 5f82d7d] nieudane proby coordinates dla cech_drw
 10 files changed, 28539 insertions(+), 40853 deletions(-)
 rewrite sage/drafty/draft.sage (63%)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git pushpush. 
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 28, done.
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Counting objects: 100% (28/28)
Counting objects: 100% (28/28), done.
Delta compression using up to 4 threads
Compressing objects:   6% (1/16)
Compressing objects:  12% (2/16)
Compressing objects:  18% (3/16)
Compressing objects:  25% (4/16)
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Compressing objects:  87% (14/16)
Compressing objects:  93% (15/16)
Compressing objects: 100% (16/16)
Compressing objects: 100% (16/16), done.
Writing objects:   6% (1/16)
Writing objects:  12% (2/16)
Writing objects:  18% (3/16)
Writing objects:  25% (4/16)
Writing objects:  31% (5/16)
Writing objects:  37% (6/16)
Writing objects:  43% (7/16)
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Writing objects:  56% (9/16)
Writing objects:  62% (10/16)
Writing objects:  68% (11/16)
Writing objects:  75% (12/16)
Writing objects:  81% (13/16)
Writing objects:  87% (14/16)
Writing objects:  93% (15/16)
Writing objects: 100% (16/16)
Writing objects: 100% (16/16), 200.65 KiB | 1.44 MiB/s, done.
Total 16 (delta 12), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   b79484b..5f82d7d  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: 2021 De Rham/DeRhamComputation[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
OSError                                   Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach)
    242         break
    243 else:
--> 244     raise IOError('did not find file %r to load or attach' % filename)
    246 ext = os.path.splitext(fpath)[1].lower()
    247 if ext == '.py':

OSError: did not find file 'init.sage' to load or attach
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd sagesage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltrix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0] - 4*b[0] - 6*b[1]

[?7h[?12l[?25h[?2004l[?7h(V(((x^3 + x^2 + x)/(x*y + y)) dx), V(((2*x^2 + 1)/x^2)*y), V(((x^3 + x^2 + x)/(x*y + y)) dx) + dV([((x^2 + 2)/x^2)*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[0] - 4*b[0] - 6*b[1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (b[0] - 4*b[0] - 6*b[1]).reduce()

[?7h[?12l[?25h[?2004l[?7h(V(((x^3 + x^2 + x)/(x*y + y)) dx) + dV([y]), [0], V(((x^3 + x^2 + x)/(x*y + y)) dx) + dV([y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[0] - 4*b[0] - 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (b[0] - 4*b[0] - 6*b[1]).reduce().omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[0] - 4*b[0] - 6*b[1]).reduce().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[0] - 4*b[0] - 6*b[1]).reduce().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lb[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lab[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7lub[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7ltb[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7lob[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7lmb[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l(b[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([]) - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]) - 4*b[0] - 6*b[1]

[?7h[?12l[?25h[?2004l[?7h(V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V(((2*x^3 + 2*x^2 + 1)/(x^3 + x^2))*y), V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([((x^2 + 2)/x^2)*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(autom(b[0]) - 4*b[0] - 6*b[1])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce()

[?7h[?12l[?25h[?2004l[?7h(V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^2 + x))*y]), [0], V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(autom(b[0]) - 4*b[0] - 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce().frobenius()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 (autom(b[Integer(0)]) - Integer(4)*b[Integer(0)] - Integer(6)*b[Integer(1)]).reduce().frobenius()

AttributeError: 'superelliptic_drw_cech' object has no attribute 'frobenius'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(autom(b[0]) - 4*b[0] - 6*b[1]).reduce().frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lofrobenius()[?7h[?12l[?25h[?25l[?7lmfrobenius()[?7h[?12l[?25h[?25l[?7lefrobenius()[?7h[?12l[?25h[?25l[?7lgfrobenius()[?7h[?12l[?25h[?25l[?7lafrobenius()[?7h[?12l[?25h[?25l[?7l0frobenius()[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce().omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h(1/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(autom(b[0]) - 4*b[0] - 6*b[1]).reduce().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce().f

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(autom(b[0]) - 4*b[0] - 6*b[1]).reduce().f[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()omega0.frobenius()[?7h[?12l[?25h[?25l[?7l(omega0.frobenius()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (autom(b[0]) - 4*b[0] - 6*b[1]).omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^2 - x + 1)/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lTrue[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: True == 1

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lre[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].is_regular()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 b[Integer(0)].is_regular()

File <string>:348, in is_regular(self)

AttributeError: 'superelliptic_form' object has no attribute 'is_regular_on_U8'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].is_regular([?7h[?12l[?25h[?25l[?7lsage: b[0].is_regular()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].is_regular()[?7h[?12l[?25h[?25l[?7l1].is_regular()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[1].is_regular()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[0]) - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7lb[0]) - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*b[1][?7h[?12l[?25h[?25l[?7l4*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]) - 4*b[0] - 4*b[1][?7h[?12l[?25h[?25l[?7l1]) - 4*b[0] - 4*b[1][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(b[1]) - 4*b[0] - 4*b[1]

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x + 1)/(x*y)) dx) + dV([2/x*y]), [(1/(x^2 + x))*y] + V(((x^3 + x^2 + 2)/(x^3 + x^2))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^8 - x^6 - x^5 - x^4 - x^2 - x + 1)/(x^6*y - x^4*y + x^3*y - x*y)) dx) + dV([((2*x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 2)/(x^7 + 2*x^5 + x^4 + 2*x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[1]) - 4*b[0] - 4*b[1][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b[1]).is_regular()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[1]).is_regular()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).is_regular()[?7h[?12l[?25h[?25l[?7l0]).is_regular()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).is_regular()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).is_regular()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([].is_regular()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].is_regular()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].is_regular()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).is_regular()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: autom(b[0])

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:17, in <module>

File <string>:340, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(b[0])[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7lautom(b[0])[?7h[?12l[?25h[?25l[?7lsage: autom(b[0])

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 1)
omega8, omega8_lift.r() (1/y) dx (1/y) dx
(0, x)
omega8, omega8_lift.r() ((-1)/(x*y)) dx ((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0])[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm(b[0])[?7h[?12l[?25h[?25l[?7l().is_regular()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).is_regular()

[?7h[?12l[?25h[?2004l1 1 0 1
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).is_regular()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().is_regular()[?7h[?12l[?25h[?25l[?7lreduce(), 4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).r()

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b[0])

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7lbb[0].function.numerator().exponents()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion(pt = (-1, 0))[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lfn[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn())

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [32], in <cell line: 1>()
----> 1 om1 = C.y.teichmuller().diffn() + (Integer(2)*C.x*C.y).verschiebung().diffn() + (C.x**Integer(5)*(C.y).diffn())

File <string>:231, in __add__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'h1'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuprelliptic_drw_cech(xi0, 3*xi1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_cech(xi0, 3*xi1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3*xi1)[?7h[?12l[?25h[?25l[?7l, 3*xi1)[?7h[?12l[?25h[?25l[?7l, 3*xi1)[?7h[?12l[?25h[?25l[?7lo, 3*xi1)[?7h[?12l[?25h[?25l[?7lm, 3*xi1)[?7h[?12l[?25h[?25l[?7l1, 3*xi1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.y)/(C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).teichmuller())

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).teichmuller())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.is_regular()

[?7h[?12l[?25h[?2004l1 0 1 0
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.r()

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 1/x*y, ((x^2 + x + 1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lxi.r()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7lv())[?7h[?12l[?25h[?25l[?7le())[?7h[?12l[?25h[?25l[?7lr())[?7h[?12l[?25h[?25l[?7ls())[?7h[?12l[?25h[?25l[?7lc())[?7h[?12l[?25h[?25l[?7lh())[?7h[?12l[?25h[?25l[?7li())[?7h[?12l[?25h[?25l[?7le())[?7h[?12l[?25h[?25l[?7lb())[?7h[?12l[?25h[?25l[?7lu())[?7h[?12l[?25h[?25l[?7ln())[?7h[?12l[?25h[?25l[?7lg())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7lC.de_rham_bass()[?7h[?12l[?25h[?25l[?7lxi.r()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lsage: xi.is_regular()

[?7h[?12l[?25h[?2004l1 1 1 1
[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0])[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_regular()[?7h[?12l[?25h[?25l[?7ls_regular()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(xi).is_regular()

[?7h[?12l[?25h[?2004l1 1 0 1
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(xi).is_regular()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(xi).omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7lsage: x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(autom(b[0]) - 4*b[0] - 6*b[1]).omega0.frobenius()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-x^3 + x^2 - x + 1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^3 + x^2 - x + 1).quo_rem(x^2 + x)

[?7h[?12l[?25h[?2004l[?7h(2*x + 2, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(xi).omega0.frobenius()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 autom(x)

File <string>:389, in autom(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'curve'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l).omega0.frobenius()[?7h[?12l[?25h[?25l[?7l().omega0.frobenius()[?7h[?12l[?25h[?25l[?7lsage: autom(xi).omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(xi).omega0.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(xi)

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^4 - x^2 - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^4 - x^2 - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li.is_regular()[?7h[?12l[?25h[?25l[?7lsage: xi

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 - x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 - x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lautom(xi)[?7h[?12l[?25h[?25l[?7l().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(-x^3 + x^2 - x + 1).quo_rem(x^2 + x)[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lautom(xi).omega0.frobenius()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7lC.de_rham_bass()[?7h[?12l[?25h[?25l[?7lxi.r()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).teichmuller())[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmulle().diffn() + 2*C.x*y.versiebung.diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lxi = superelliptic_dw_cech(om1, (C.y)/(x).teimuller)[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lxi = superellptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7lautom(xi).is_regular()[?7h[?12l[?25h[?25l[?7lomega0.frobenius()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7l(-x^3 + x^2 - x + 1).quo_rem(x^2 + x)[?7h[?12l[?25h[?25l[?7lautom(x)[?7h[?12l[?25h[?25l[?7l(i).omega0.frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^3 + x^2 - x + 1).quo_rem(x^2 + x)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (-1/2)%9

[?7h[?12l[?25h[?2004l[?7h4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[1] d[x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l/C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l2C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 1/2*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[2] d[x] + V((x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1/2)%9[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (1/2^3)%9

[?7h[?12l[?25h[?2004l[?7h8
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[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 teichmuller_lift(Integer(2), Integer(3))

NameError: name 'teichmuller_lift' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller_lift(2, 3)[?7h[?12l[?25h[?25l[?7l(2^3)%9[?7h[?12l[?25h[?25l[?7l1/2^3)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[2] d[x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l2C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[2] d[x] + V((x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l12*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l/2*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-1/2)*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-1/2)*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[1] d[x] + V((-x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1/2)*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lteichmuller_ift(2, 3)[?7h[?12l[?25h[?25l[?7l(2^3)%9[?7h[?12l[?25h[?25l[?7l1/2^3)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: 1/2*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[2] d[x] + V((x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1/2)*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l1/2^3)%9[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (1/2)%9

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: 5^3-5

[?7h[?12l[?25h[?2004l[?7h120
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l5^3-5[?7h[?12l[?25h[?25l[?7l(1/2)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: 1/2*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[2] d[x] + V((-x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 5*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[2] d[x] + V((-x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lab[0][?7h[?12l[?25h[?25l[?7lub[0][?7h[?12l[?25h[?25l[?7ltb[0][?7h[?12l[?25h[?25l[?7lob[0][?7h[?12l[?25h[?25l[?7lmb[0][?7h[?12l[?25h[?25l[?7l(b[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().r()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lregular()[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).is_regular()

[?7h[?12l[?25h[?2004l1 1 0 1
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).is_regular()[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l5*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l1/2*Cx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l5^3-5[?7h[?12l[?25h[?25l[?7l(1/2)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-1/2)*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lteichmuller_ift(2, 3)[?7h[?12l[?25h[?25l[?7l(2^3)%9[?7h[?12l[?25h[?25l[?7l1/2^3)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-1/2)%9[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lautom(xi)[?7h[?12l[?25h[?25l[?7l().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(-x^3 + x^2 - x + 1).quo_rem(x^2 + x)[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lautom(xi).omega0.frobenius()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7lC.de_rham_bass()[?7h[?12l[?25h[?25l[?7lxi.r()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).teichmuller())[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmulle().diffn() + 2*C.x*y.versiebung.diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().verschiebung()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn())[?7h[?12l[?25h[?25l[?7l().verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lautom(b[0]).s_regular()[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l5*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l1/2*Cx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l5^3-5[?7h[?12l[?25h[?25l[?7l(1/2)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-1/2)*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lteichmuller_ift(2, 3)[?7h[?12l[?25h[?25l[?7l(2^3)%9[?7h[?12l[?25h[?25l[?7l1/2^3)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-1/2)%9[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lautom(xi)[?7h[?12l[?25h[?25l[?7l().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(-x^3 + x^2 - x + 1).quo_rem(x^2 + x)[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lautom(xi).omega0.frobenius()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lsage: xi.is_regular()

[?7h[?12l[?25h[?2004l1 1 1 1
[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).is_regular()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lxi)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().omega0.frobenius()[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(xi).is_regular()

[?7h[?12l[?25h[?2004l1 1 0 1
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(xi).is_regular()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(x^3 - x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 auxilliary_derivative(x**Integer(3) - x)

File <string>:136, in auxilliary_derivative(P)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 't'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lC))[?7h[?12l[?25h[?25l[?7lX))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l.))[?7h[?12l[?25h[?25l[?7lx))[?7h[?12l[?25h[?25l[?7l^))[?7h[?12l[?25h[?25l[?7l3))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l-))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7lC))[?7h[?12l[?25h[?25l[?7l.))[?7h[?12l[?25h[?25l[?7lx))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((C.x^3 - C.x).teichmuller())

[?7h[?12l[?25h[?2004l[?7h[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x^3 - C.x).teichmuller()

[?7h[?12l[?25h[?2004l[?7h[x^3 + 2*x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuller()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7ltom(xi).is_egular()[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmulle().diffn() + 2*C.x*y.verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lautom(b[0]).s_regular()[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l5*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l1/2*Cx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l5^3-5[?7h[?12l[?25h[?25l[?7l(1/2)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-1/2)*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lteichmuller_ift(2, 3)[?7h[?12l[?25h[?25l[?7l(2^3)%9[?7h[?12l[?25h[?25l[?7l1/2^3)%9[?7h[?12l[?25h[?25l[?7l1/2*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-1/2)%9[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuller()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l() auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(() auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(()) auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l-)) auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l)) auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-()) auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC)) auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l.)) auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7ly)) auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.) auxiliary_derivative(C.x^3 - 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C.x).teichmuller())

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [77], in <cell line: 1>()
----> 1 (-(C.y).teichmuller())**(-Integer(1))* auxilliary_derivative((C.x**Integer(3) - C.x).teichmuller())

File /ext/sage/9.7/src/sage/rings/integer.pyx:2195, in sage.rings.integer.Integer.__pow__()
   2193         return coercion_model.bin_op(left, right, operator.pow)
   2194     # left is a non-Element: do the powering with a Python int
-> 2195     return left ** int(right)
   2196 
   2197 cpdef _pow_(self, other):

TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_witt' and 'int'
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C.x).teichmuller())

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 - x^3)/y) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-((C.y)^(-1)).teichmuller())* auxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-((C.y)^(-1)).teichmuller())* auxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-(C.y)^(-1).teichmuler())* auxiliary_derivative(C.x^3 - C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-((C.y)^(-1)).teichmuller())* auxilliary_derivative((C.x^3 - C.x).teichmuller())).frobenius()

[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [81], in <cell line: 1>()
----> 1 (C.y**Integer(2)).teichmuller().diffn() == (C.x**Integer(3) - C.x).teichmuller().diffn()

File <string>:172, in __eq__(self, other)

File <string>:42, in __eq__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C.y^2

[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l(C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) [2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5])
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 (C.y**Integer(2)).teichmuller().diffn() == (C.x**Integer(3) - C.x).teichmuller().diffn()

File <string>:174, in __eq__(self, other)

File <string>:42, in __eq__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 2*(C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7lY(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7ly(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7lt(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7le(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7li(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7lc(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7lh(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7lm(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7lu(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7ll(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7ll(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7le(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7lr(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l((C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l)(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*(C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuler() * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().teichmuler() * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004ldy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lw)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lw)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ld) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7ly) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l_) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7lw) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l ) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l=) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l ) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7lC) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l.) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7ld) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7ly) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l_) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7lw) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) * (C.y).teichmuler().difn() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ldy_w= C.dy_w) == (C.x^3 - C.x).techmuller().diffn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [91], in <cell line: 1>()
----> 1 Integer(2)*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w) == (C.x**Integer(3) - C.x).teichmuller().diffn(dy_w = C.dy_w)

File <string>:99, in diffn(self, dy_w)

File <string>:230, in __add__(self, other)

AttributeError: 'NoneType' object has no attribute 'h1'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7lsage: C.dy_w

[?7h[?12l[?25h[?2004l[?7h<bound method dy_w of Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dy_w[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dy_w()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dy_w()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(() = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w()[?7h[?12l[?25h[?25l[?7l(()) = (C.x^3 - C.x).teichmuler().difn(dy_w = C.dy_w()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7lsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w()) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w())

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w()) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w())[?7h[?12l[?25h[?25l[?7lC.dy_w()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7l) ==(C.x^3 - C.x).teichmuller().dffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.diffn( == (C.x^3 - Cx).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(C.y^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l(C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l((-((C.y)^(-1)).teichmuller())* auxilliary_derivative((C.x^3 - C.x).teichmuller())).frobenius()[?7h[?12l[?25h[?25l[?7l-(C.y)^(-1).teichmuler()* auxiliary_derivative(C.x^3 - C.x).teichmuler())[?7h[?12l[?25h[?25l[?7lC.y).teichmuller())^(-1)* auxilliary_derivative((C.x^3 -C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuller()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7ltom(xi).is_egular()[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmulle().diffn() + 2*C.x*y.verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lxi = superelliptic_dw_cech(om1, (C.y)/(x).verschiebung())[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7lautom(xi).is_regular()[?7h[?12l[?25h[?25l[?7lxilliary_deivative(x^3 - x)[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l(C.x^3 - C.x).teichmuller()[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-(C.y).teichmuller())^(-1)* auxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w()) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w())[?7h[?12l[?25h[?25l[?7lC.dy_w()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w)[?7h[?12l[?25h[?25l[?7lC.dy_w[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w()) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w())[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 









 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(xi).is_egular()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(om1)

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^4 - x^2 - x + 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()][?7h[?12l[?25h[?25l[?7lsage: autom(om1).frobenius()]

[?7h[?12l[?25h[?2004l  Input In [98]
    autom(om1).frobenius()]
                          ^
SyntaxError: unmatched ']'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1).frobenius()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(om1).frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1).frobenius()[?7h[?12l[?25h[?25l[?7l()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn().frobenius()

[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.x*C.y).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (2*C.x*C.y).verschiebung().diffn().frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^3)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^5*(C.y).diffn()).verschiebung().frobenius()

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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1).frobenius()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom1).frobenius()[?7h[?12l[?25h[?25l[?7lsage: autom(om1).frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y])
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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom((C.x^5*(C.y).diffn()).verschiebung()).frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.y).difn().verschiebung().frobenius()[?7h[?12l[?25h[?25l[?7l(C.y).difn().verschiebung().frobenius()[?7h[?12l[?25h[?25l[?7l(C.y).difn().verschiebung().frobenius()[?7h[?12l[?25h[?25l[?7l(C.y).difn().verschiebung().frobenius()[?7h[?12l[?25h[?25l[?7l(C.y).difn().verschiebung().frobenius()[?7h[?12l[?25h[?25l[?7l(C.y).difn().verschiebung().frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(().frobenius()[?7h[?12l[?25h[?25l[?7l().frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l(().frobenius()[?7h[?12l[?25h[?25l[?7l(().frobenius()[?7h[?12l[?25h[?25l[?7l().frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l(().frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l).frobenius()[?7h[?12l[?25h[?25l[?7l().frobenius()[?7h[?12l[?25h[?25l[?7l().frobenius()[?7h[?12l[?25h[?25l[?7l(().frobenius()[?7h[?12l[?25h[?25l[?7l(()).frobenius()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lC)).frobenius()[?7h[?12l[?25h[?25l[?7l.)).frobenius()[?7h[?12l[?25h[?25l[?7ly)).frobenius()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.).frobenius()[?7h[?12l[?25h[?25l[?7ld).frobenius()[?7h[?12l[?25h[?25l[?7li).frobenius()[?7h[?12l[?25h[?25l[?7lf).frobenius()[?7h[?12l[?25h[?25l[?7lf).frobenius()[?7h[?12l[?25h[?25l[?7ln).frobenius()[?7h[?12l[?25h[?25l[?7l()).frobenius()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().difn().frobenius()[?7h[?12l[?25h[?25l[?7l.difn().frobenius()[?7h[?12l[?25h[?25l[?7ldifn().frobenius()[?7h[?12l[?25h[?25l[?7lt.difn().frobenius()[?7h[?12l[?25h[?25l[?7le.difn().frobenius()[?7h[?12l[?25h[?25l[?7li.difn().frobenius()[?7h[?12l[?25h[?25l[?7lc.difn().frobenius()[?7h[?12l[?25h[?25l[?7lh.difn().frobenius()[?7h[?12l[?25h[?25l[?7lm.difn().frobenius()[?7h[?12l[?25h[?25l[?7lu.difn().frobenius()[?7h[?12l[?25h[?25l[?7ll.difn().frobenius()[?7h[?12l[?25h[?25l[?7ll.difn().frobenius()[?7h[?12l[?25h[?25l[?7le.difn().frobenius()[?7h[?12l[?25h[?25l[?7lr.difn().frobenius()[?7h[?12l[?25h[?25l[?7l(.difn().frobenius()[?7h[?12l[?25h[?25l[?7l().difn().frobenius()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom((C.y).teichmuller().diffn()).frobenius()

[?7h[?12l[?25h[?2004l[?7h((x^5 + x^4 - x^3 - x^2 + 1)/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.y.teich[?7h[?12l[?25h[?25l[?7luC.y.teich[?7h[?12l[?25h[?25l[?7ltC.y.teich[?7h[?12l[?25h[?25l[?7loC.y.teich[?7h[?12l[?25h[?25l[?7lmC.y.teich[?7h[?12l[?25h[?25l[?7l(C.y.teich[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: autom(C.y.teichmuller().diffn())

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 + 1)/(x^2*y - x*y)) dx) + dV([((x^3 + 1)/(x^2 + 2*x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.y.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: autom(C.y.teichmuller().diffn()) - C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((x^6 + x^4 - x^2 + x - 1)/(x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^2 + x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.y.teichmuller().diffn()) - C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.y).teichmuller().diffn()).frobenius()[?7h[?12l[?25h[?25l[?7lx^5*(C.y).diffn()).verschiebung()).frobenius()[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lautom(om1).frobenius()[?7h[?12l[?25h[?25l[?7lom1.frbenius()[?7h[?12l[?25h[?25l[?7l(C.x^5*(C.y).diffn()).verschiebung().frobenius()[?7h[?12l[?25h[?25l[?7l2*C.xC.y).verschiebung().dffn().frobenius()[?7h[?12l[?25h[?25l[?7lC.y.teichmull().diff().frobeius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lautom(om1).frobenius()[?7h[?12l[?25h[?25l[?7l()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.is_regular()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [113], in <cell line: 1>()
----> 1 om1.is_regular()

AttributeError: 'superelliptic_drw_form' object has no attribute 'is_regular'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.is_regular()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7lfrobnius()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom1.frobenius()[?7h[?12l[?25h[?25l[?7luom1.frobenius()[?7h[?12l[?25h[?25l[?7ltom1.frobenius()[?7h[?12l[?25h[?25l[?7lom1.frobenius()[?7h[?12l[?25h[?25l[?7lmom1.frobenius()[?7h[?12l[?25h[?25l[?7l(om1.frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().frobenius()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(om1).frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1).frobenius()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[0]).is_reglar()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]).is_regular()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]).is_regular()[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).is_regular()

[?7h[?12l[?25h[?2004l1 1 1 1
[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).is_regular()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7les()[?7h[?12l[?25h[?25l[?7lsage: autom(b[0]).coordinates()

[?7h[?12l[?25h[?2004l(1, 0)
aux before reduce (V(((-1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
aux V(smth) (V(((-1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [118], in <cell line: 1>()
----> 1 autom(b[Integer(0)]).coordinates()

File <string>:339, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m '""P"o"p"r"a"w"i"o"n"y" "d"y"_"w" "o"r"a"z" "[1@ [1@i[1@ [1@s[1@p[1@r[1@a[1@d[1@z[1@w[1@d[1@z[1@o[1@n[1@ya"u"t"o"m"."
[master cc45757] Poprawiony i sprawdzony dy_w oraz autom.
 4 files changed, 800 insertions(+), 17 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jganrke     arnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 17, done.
Counting objects:   5% (1/17)
Counting objects:  11% (2/17)
Counting objects:  17% (3/17)
Counting objects:  23% (4/17)
Counting objects:  29% (5/17)
Counting objects:  35% (6/17)
Counting objects:  41% (7/17)
Counting objects:  47% (8/17)
Counting objects:  52% (9/17)
Counting objects:  58% (10/17)
Counting objects:  64% (11/17)
Counting objects:  70% (12/17)
Counting objects:  76% (13/17)
Counting objects:  82% (14/17)
Counting objects:  88% (15/17)
Counting objects:  94% (16/17)
Counting objects: 100% (17/17)
Counting objects: 100% (17/17), done.
Delta compression using up to 4 threads
Compressing objects:  11% (1/9)
Compressing objects:  22% (2/9)
Compressing objects:  33% (3/9)
Compressing objects:  44% (4/9)
Compressing objects:  55% (5/9)
Compressing objects:  66% (6/9)
Compressing objects:  77% (7/9)
Compressing objects:  88% (8/9)
Compressing objects: 100% (9/9)
Compressing objects: 100% (9/9), done.
Writing objects:  11% (1/9)
Writing objects:  22% (2/9)
Writing objects:  33% (3/9)
Writing objects:  44% (4/9)
Writing objects:  55% (5/9)
Writing objects:  66% (6/9)
Writing objects:  77% (7/9)
Writing objects:  88% (8/9)
Writing objects: 100% (9/9)
Writing objects: 100% (9/9), 15.99 KiB | 207.00 KiB/s, done.
Total 9 (delta 8), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   5f82d7d..cc45757  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7lsage: b

[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
 ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion((C.x)^3 + C.one, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), [1/x*y], [((x + 2)/(x^3 + x^2))*y] d[x] + V(((-x^5 + x^4 - x^3 + x - 1)/(x^2*y)) dx) + dV([(1/(x + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta1.is_regular()

[?7h[?12l[?25h[?2004l1 0 1 0
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7let1.is_regular([?7h[?12l[?25h[?25l[?7lsage: eta1.is_regular()

[?7h[?12l[?25h[?2004l1 1 1 1
[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.is_regular()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7l2.is_regular()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta2.is_regular()

[?7h[?12l[?25h[?2004l1 1 1 1
[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]-[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: b[0]-eta1

[?7h[?12l[?25h[?2004l[?7h(V((x^3/y) dx), [0], V((x^3/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0]-eta1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[] - 4*b[0] - 6*b[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: b[0] == eta1

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0] == eta1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].is_regular()[?7h[?12l[?25h[?25l[?7lomega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: b[0].omega0 == eta1.omega0

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega0 == eta1.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = eta1.omega8[?7h[?12l[?25h[?25l[?7l8 = eta1.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].omega8 == eta1.omega8

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].omega8 == eta1.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8[?7h[?12l[?25h[?25l[?7l2.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].omega8 = eta2.omega8[?7h[?12l[?25h[?25l[?7l1].omega8 = eta2.omega8[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b[1].omega8 == eta2.omega8

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[1].omega8 == eta2.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[1].omega8 == eta2.omega8[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: b[1] - eta2

[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[1] - eta2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[1] - eta2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[1] - eta2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (b[1] - eta2).omega0.omega.cartier()

[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: om3 = C.y.verschiebung().diffn() + mul

 mul                      multinomial              multiples               

 mult_by_p                multinomial_coefficients multiplicative_order    

 multi_graphics           multiple                                         



 [?7h[?12l[?25h[?25l[?7l

 mul                     





 <unknown> [?7h[?12l[?25h[?25l[?7lt_by_p

 mul                     

 mult_by_p               [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lD)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: om3 = C.y.verschiebung().diffn() + mult_by_p(C.x*(C.y).diffn())

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lom3 = C.y.verschiebung().diffn() + mult_by_p(C.x*(C.y).diffn())[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: ome3

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 ome3

NameError: name 'ome3' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lome3[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3 = C.y.verschiebung().diffn() + mult_by_p(C.x*(C.y).diffn())[?7h[?12l[?25h[?25l[?7lsage: om3

[?7h[?12l[?25h[?2004l[?7hV((x^4/(x^2*y - y)) dx) + dV([y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom3[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om3.reduce()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 om3.reduce()

AttributeError: 'superelliptic_drw_form' object has no attribute 'reduce'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom3.reduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le3[?7h[?12l[?25h[?25l[?7l3 = C.y.verschiebung().diffn() + mult_by_p(C.x*(C.y).diffn())[?7h[?12l[?25h[?25l[?7l(b[1]- eta2).omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: (b[1] - eta2).omega0 - om3

[?7h[?12l[?25h[?2004l[?7hV(((x^10 + x^8 + x^6 - x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([2*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[1] - eta2).omega0 - om3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((b[1] - eta2).omega0 - om3)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((b[1] - eta2).omega0 - om3).frobenius()

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((b[1] - eta2).omega0 - om3).frobenius()[?7h[?12l[?25h[?25l[?7lb[1] - eta2).omega0 - om3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l om3[?7h[?12l[?25h[?25l[?7l+ om3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (b[1] - eta2).omega0 + om3

[?7h[?12l[?25h[?2004l[?7hV(((x^10 + x^8 + x^6 + x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[1] - eta2).omega0 + om3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega.cartier()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (b[1] - eta2).omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[1] - eta2).omega0.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (b[1] - eta2)

[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[1] - eta2)[?7h[?12l[?25h[?25l[?7l().omega0.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (b[1] - eta2).omega0.cartier()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 (b[Integer(1)] - eta2).omega0.cartier()

AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[1] - eta2).omega0.cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7locartier()[?7h[?12l[?25h[?25l[?7lmcartier()[?7h[?12l[?25h[?25l[?7lecartier()[?7h[?12l[?25h[?25l[?7lgcartier()[?7h[?12l[?25h[?25l[?7lacartier()[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (b[1] - eta2).omega0.omega.cartier()

[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldy_w()[?7h[?12l[?25h[?25l[?7lerham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8_regular (0, 1)
omega0_regular (0, x)
omega8_regular (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b[1] - eta2).omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lC.x^5*(C.y).diffn()).vrschiebung.frobenius()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x*C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x*C.y)^(-1)*C.dx).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + O(t^12)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsoln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld_patch[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7lsage: second_patch((C.x*C.y)^(-1)*C.dx))

[?7h[?12l[?25h[?2004l  Input In [30]
    second_patch((C.x*C.y)**(-Integer(1))*C.dx))
                                               ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch((C.x*C.y)^(-1)*C.dx))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch((C.x*C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[1] - eta2[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0.omg8 == eta1.omega8[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1 - eta2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].omg8 == eta2.omega8[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: b[1]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[1][?7h[?12l[?25h[?25l[?7l[].omega8 == eta2.omega8[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[1].is_regular()

[?7h[?12l[?25h[?2004l1 1 1 1
[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7lude_rham_wit_lift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7lxde_rham_wit_lift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = de_rham_witt_lift(C.de_rham_basis()[1])

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = de_rham_witt_lift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lfn[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 aux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (Integer(2)*(C.x)**(-Integer(1))).teichmuller()*(C.y/C.x**Integer(2)).teichmuller().diffn() + (C.y/C.x).diffn()

File <string>:230, in __add__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'h1'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ltdifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lidifn()[?7h[?12l[?25h[?25l[?7lcdifn()[?7h[?12l[?25h[?25l[?7lhdifn()[?7h[?12l[?25h[?25l[?7lmdifn()[?7h[?12l[?25h[?25l[?7ludifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lrdifn()[?7h[?12l[?25h[?25l[?7l(difn()[?7h[?12l[?25h[?25l[?7l()difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = de_rham_witt_ift(C.de_rham_basis()[1])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux == aux1

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux == aux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7hV(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git pushcommit -m "Poprawiony i sprawdzony dy_w oraz autom."pushsage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gicd ..sagegit pushcommit -m "Poprawiony i sprawdzony dy_w oraz autom."
add -udra -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git git commit -m "przeniesione pliki"
[master 7bcfa5d] przeniesione pliki
 6 files changed, 208 insertions(+), 516 deletions(-)
 delete mode 100644 sage/drafty/second_patch.sage
 delete mode 100644 sage/drafty/superelliptic_drw.sage
 delete mode 100644 sage/superelliptic/decomposition_into_g0_g8.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/drafty/superelliptic_drw/superelliptic_drw.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_drw.sageencond_patch.sage sage/superelliptic_drw/decomposition_into_g0_g8.sage 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/second_patch.sage sage/superelliptic_drw/decomposition_into_g0_g8.sage uperelliptic_drw.sage
commit -m "przeniesione pliki" "2"
[master b03c679] przeniesione pliki 2
 3 files changed, 515 insertions(+)
 create mode 100644 sage/superelliptic_drw/decomposition_into_g0_g8.sage
 create mode 100644 sage/superelliptic_drw/second_patch.sage
 create mode 100644 sage/superelliptic_drw/superelliptic_drw.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m "przeniesione pliki 2"git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_
superelliptic_drw_cech.sage  superelliptic_drw_form.sage  superelliptic_drw_tests/     
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_
superelliptic_drw_cech.sage  superelliptic_drw_form.sage  superelliptic_drw_tests/     
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_form.sage sage/superelliptic_drw/de_rham_witt_lift.sage sage/superelliptic_drw/automorphism.sage 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git addd  -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m "superelliptic drw podzielone na wiecej pilikow"
[master ce0ac0d] superelliptic drw podzielone na wiecej plikow
 8 files changed, 442 insertions(+), 421 deletions(-)
 create mode 100644 sage/superelliptic_drw/automorphism.sage
 create mode 100644 sage/superelliptic_drw/de_rham_witt_lift.sage
 delete mode 100644 sage/superelliptic_drw/superelliptic_drw.sage
 create mode 100644 sage/superelliptic_drw/superelliptic_drw_cech.sage
 create mode 100644 sage/superelliptic_drw/superelliptic_drw_form.sage
 create mode 100644 sage/superelliptic_drw/superelliptic_witt.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 31, done.
Counting objects:   3% (1/31)
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Counting objects: 100% (31/31)
Counting objects: 100% (31/31), done.
Delta compression using up to 4 threads
Compressing objects:   4% (1/24)
Compressing objects:   8% (2/24)
Compressing objects:  12% (3/24)
Compressing objects:  16% (4/24)
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Compressing objects: 100% (24/24), done.
Writing objects:   4% (1/24)
Writing objects:   8% (2/24)
Writing objects:  12% (3/24)
Writing objects:  16% (4/24)
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Writing objects:  37% (9/24)
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Writing objects:  45% (11/24)
Writing objects:  54% (13/24)
Writing objects:  58% (14/24)
Writing objects:  62% (15/24)
Writing objects:  66% (16/24)
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Writing objects: 100% (24/24)
Writing objects: 100% (24/24), 11.54 KiB | 168.00 KiB/s, done.
Total 24 (delta 17), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   cc45757..ce0ac0d  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage/
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7hV(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aux.omega

[?7h[?12l[?25h[?2004l'[?7h((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lomea0_omega8((C.x)(-2)*C.dx)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega0_omega8((C.x)^(-2)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)

[?7h[?12l[?25h[?2004l[?7h(((-x^8 + x^6 - 1)/y) dx, ((-x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/de_rham_witt_lift.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1] == aux.omega

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1] == aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l decomposition_omega0_omega8(aux.omega)[1] = aux.omega[?7h[?12l[?25h[?25l[?7l+ decomposition_omega0_omega8(aux.omega)[1] = aux.omega[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] == aux.omega

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] == aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l- aux.omega[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] -  aux.omega

[?7h[?12l[?25h[?2004l[?7h((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] -  aux.omega[?7h[?12l[?25h[?25l[?7l==[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l[]aux.omega[?7h[?12l[?25h[?25l[?7l[]- aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]- aux.omega

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]- aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] aux.omega[?7h[?12l[?25h[?25l[?7l[]= aux.omega[?7h[?12l[?25h[?25l[?7l= aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom3.reduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form

[?7h[?12l[?25h[?2004l[?7h(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.omega[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux.omega.reduce().form

[?7h[?12l[?25h[?2004l[?7h(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7laux.omega.reduce().form[?7h[?12l[?25h[?25l[?7l(decposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecompsition_mega0_omega8(ux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecmposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecompositin_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7lecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[1].expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^4 + 2*t^8 + t^12 + O(t^14)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0]

[?7h[?12l[?25h[?2004l[?7h((-x^8 + x^6 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.omega.reduce().form[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7hV((((2*x^18 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^4 + 2*x^2 + 2)/(x^13 + x^11 + x^9))*y) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.omega.reduce().form[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: aux.h2

[?7h[?12l[?25h[?2004l[?7h((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: decomposition

 decomposition                 decomposition_g0_g8_pth_power

 decomposition_g0_g8           decomposition_omega0_omega8  





 [?7h[?12l[?25h[?25l[?7l_omega0_omega8(aux.omega)[0][?7h[?12l[?25h[?25l[?7l

 decomposition                



 <unknown> [?7h[?12l[?25h[?25l[?7l_g0_g8

 decomposition                

 decomposition_g0_g8          [?7h[?12l[?25h[?25l[?7l((2*C.one/(C.x^2 + C.x))*C.y)





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h2)

[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)*y, ((x^4 + x^2 + 1)/x^6)*y, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h2)[0] - decomposition_g0_g8(aux.h2)[1] == aux.h2

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[0] - decomposition_g0_g8(aux.h2)[1] == aux.h2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l[]decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l[decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l()decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l(decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7lecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h2)[1].expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + t^13 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega.reduce().form[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aux.omega

[?7h[?12l[?25h[?2004l[?7h(((2*x^18 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^4 + 2*x^2 + 2)/(x^13 + x^11 + x^9))*y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: load('super

 super                  superelliptic_cech     superelliptic_drw_form superelliptic_witt    

 superelliptic          superelliptic_drw/     superelliptic_form     supersingular_D       

 superelliptic/         superelliptic_drw_cech superelliptic_function supersingular_j       



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 super                 





 <unknown> [?7h[?12l[?25h[?25l[?7lelliptic

 super                 

 superelliptic         [?7h[?12l[?25h[?25l[?7l/



 superelliptic         

 superelliptic/        [?7h[?12l[?25h[?25l[?7l_cech

 superelliptic_cech    



 superelliptic/        [?7h[?12l[?25h[?25l[?7ldrw/

 superelliptic_cech    

 superelliptic_drw/    [?7h[?12l[?25h[?25l[?7l_cech



 superelliptic_drw/    

 superelliptic_drw_cech[?7h[?12l[?25h[?25l[?7l/



 superelliptic_drw/    

 superelliptic_drw_cech[?7h[?12l[?25h[?25l[?7lt







[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 sup…rw/automorphism.sage             sup…rw/second_patch.sage             sup…rw/superelliptic_drw_tests/     

 sup…rw/de_rham_witt_lift.sage        sup…rw/superelliptic_drw_cech.sage   sup…rw/superelliptic_witt.sage      

 sup…rw/decomposition_into_g0_g8.sage sup…rw/superelliptic_drw_form.sage                                       [?7h[?12l[?25h[?25l[?7lautomorphism.sage

 sup…rw/automorphism.sage            





 <unknown> [?7h[?12l[?25h[?25l[?7lsecnd_atch

 sup…rw/automorphism.sage             sup…rw/second_patch.sage            [?7h[?12l[?25h[?25l[?7luperelliptic_drw_tests/

 sup…rw/second_patch.sage             sup…rw/superelliptic_drw_tests/     [?7h[?12l[?25h[?25l[?7l







[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsts/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_into_g0_g8_tests.sage[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')

[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
1
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')

[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
1
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.is_regular()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.omega[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lux.omega[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: eta2 - aux

[?7h[?12l[?25h[?2004l[?7h(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2 - aux)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (eta2 - aux).omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8 - x^6)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^8 - x^6).quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(x^5, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8 - x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7leta2 - aux).omega0.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (eta2 - aux).omega0.omega.cartier()

[?7h[?12l[?25h[?2004l[?7h((-x^3)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^8 + x^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8 + x^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^8 + x^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/y) dx[?7h[?12l[?25h[?25l[?7lC)/y) dx[?7h[?12l[?25h[?25l[?7l.)/y) dx[?7h[?12l[?25h[?25l[?7lo)/y) dx[?7h[?12l[?25h[?25l[?7ln)/y) dx[?7h[?12l[?25h[?25l[?7le)/y) dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy) dx[?7h[?12l[?25h[?25l[?7l/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly) dx[?7h[?12l[?25h[?25l[?7l.y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* dx[?7h[?12l[?25h[?25l[?7lC dx[?7h[?12l[?25h[?25l[?7l. dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lsage: (-C.x^8 + C.x^6 - C.one)/C.y)*C.dx

[?7h[?12l[?25h[?2004l  Input In [39]
    (-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y)*C.dx
                                                    ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.x^8 + C.x^6 - C.one)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-C.x^8 + C.x^6 - C.one)/C.y*C.dx

[?7h[?12l[?25h[?2004l[?7h((-x^8 + x^6 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.x^8 + C.x^6 - C.one)/C.y*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^8 + C.x^6 - C.one)/C.y*C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^8 + C.x^6 - C.one)/C.y*C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h((-x^3)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^8 + C.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^6 - C.one)/C.y*C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.r()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.reduce()

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: eta2 - aux

[?7h[?12l[?25h[?2004l[?7h(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega0.cartier()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 eta2.omega0.cartier()

AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7locartier()[?7h[?12l[?25h[?25l[?7lmcartier()[?7h[?12l[?25h[?25l[?7lecartier()[?7h[?12l[?25h[?25l[?7lgcartier()[?7h[?12l[?25h[?25l[?7lacartier()[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta2.omega0.omega.cartier()

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.reduce()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(b[0]).coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2).coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 autom(eta2).coordinates()

File <string>:63, in coordinates(self, basis)

File <string>:81, in coordinates(self)

File <string>:87, in coordinates(self)

File <string>:87, in coordinates(self)

    [... skipping similar frames: coordinates at line 87 (1097 times)]

File <string>:87, in coordinates(self)

File <string>:86, in coordinates(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:28, in __sub__(self, other)

File <string>:7, in __init__(self, C, g)

File <string>:245, in reduction_form(C, g)

File <string>:216, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))
    710 try:
--> 711     return self._element_class(self, x, y, coerce=coerce)
    712 except TypeError:
    713     if parent(x) is parent(x0):

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    113 if coerce:
    114     self.__numerator   = parent.ring()(numerator)
--> 115     self.__denominator = parent.ring()(denominator)
    116 else:
    117     self.__numerator   = numerator

File /ext/sage/9.7/src/sage/rings/fraction_field.py:506, in FractionField_generic.ring(self)
    503     s = 'FieldOfFractions(%s)' % self.ring()._magma_init_(magma)
    504     return magma._with_names(s, self.variable_names())
--> 506 def ring(self):
    507     """
    508     Return the ring that this is the fraction field of.
    509 
   (...)
    516         Multivariate Polynomial Ring in x, y over Rational Field
    517     """
    518     return self._R

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2).coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File <string>:226, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1002 try:
-> 1003     return self(str(element))
   1004 except TypeError:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    990         element = element.replace("^","**")
--> 991         element = eval(element, d, {})
    992 except (SyntaxError, NameError):

File <string>:1, in <module>

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [50], in <cell line: 1>()
----> 1 autom(eta2).coordinates()

File <string>:23, in autom(self)

File <string>:6, in __init__(self, omega0, f)

File <string>:90, in diffn(self, dy_w)

File <string>:99, in diffn(self, dy_w)

File <string>:84, in __add__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2).coordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    379 try:
--> 380     z = integer_ring.Z(value)
    381 except (TypeError, ValueError):

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    831 self.reduce()
--> 832 num = R(self.__numerator)
    833 inv_den = R(self.__denominator).inverse_of_unit()

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
   1691 for f in self.__list:
-> 1692     x = f._call_(x)
   1693 return x

File /ext/sage/9.7/src/sage/categories/map.pyx:1677, in sage.categories.map.FormalCompositeMap._call_()
   1676 
-> 1677     cpdef Element _call_(self, x):
   1678         """

File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
   1691 for f in self.__list:
-> 1692     x = f._call_(x)
   1693 return x

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1619 
-> 1620     cpdef Element _call_(self, _x):
   1621         """

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1651 if nmod_poly_degree(x._denom) != 0:
-> 1652     raise ValueError("not integral")
   1653 if nmod_poly_degree(x._numer) > 0:

ValueError: not integral

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 autom(eta2)

File <string>:23, in autom(self)

File <string>:19, in autom(self)

File <string>:13, in autom(self)

File <string>:7, in __init__(self, C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1007 try:
   1008     # now try calling the base ring's __call__ methods
-> 1009     element = self.base_ring()(element)
   1010     _p = p_NSet(sa2si(element,_ring), _ring)
   1011     return new_MP(self,_p)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    386     value = py_scalar_to_element(value)
    387 if isinstance(value, Element) and value.parent().is_exact():
--> 388     value = sage.rings.rational_field.QQ(value)
    389     z = value % self.__modulus.sageInteger
    390 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    536     """
    537     if x is not None:
--> 538         self.__set_value(x, base)
    539 
    540 def __reduce__(self):

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    624 
    625         elif hasattr(x, "_rational_"):
--> 626             set_from_Rational(self, x._rational_())
    627 
    628         elif isinstance(x, tuple) and len(x) == 2:

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_()
    782         1/2
    783     """
--> 784     return self._conversion(QQ)
    785 
    786 def _conversion(self, R):

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    830 else:
    831     self.reduce()
--> 832     num = R(self.__numerator)
    833     inv_den = R(self.__denominator).inverse_of_unit()
    834     return num * inv_den

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    536     """
    537     if x is not None:
--> 538         self.__set_value(x, base)
    539 
    540 def __reduce__(self):

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    624 
    625         elif hasattr(x, "_rational_"):
--> 626             set_from_Rational(self, x._rational_())
    627 
    628         elif isinstance(x, tuple) and len(x) == 2:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1446, in sage.rings.polynomial.polynomial_element.Polynomial._rational_()
   1444         TypeError: not a constant polynomial
   1445     """
-> 1446     return self._scalar_conversion(sage.rings.rational.Rational)
   1447 
   1448 def _symbolic_(self, R):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
   1389     if self.degree() > 0:
   1390         raise TypeError("cannot convert nonconstant polynomial")
-> 1391     return R(self.get_coeff_c(0))
   1392 
   1393 _real_double_ = _scalar_conversion

File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    536     """
    537     if x is not None:
--> 538         self.__set_value(x, base)
    539 
    540 def __reduce__(self):

File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value()
    689 
    690         else:
--> 691             raise TypeError("unable to convert {!r} to a rational".format(x))
    692 
    693     cdef void set_from_mpq(Rational self, mpq_t value):

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_()
    338     return repr(self.numer())
    339 else:
--> 340     numer_s = repr(self.numer())
    341     denom_s = repr(self.denom())
    342     if '-' in numer_s or '+' in numer_s:

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: load('sa

 sage          sage_eval     sage_mode     sample        save_session 

 sage0         sage_globals  sage_wraps    sandpiles                  

 sage0_version sage_input    sageobj       save                       



 [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ler

 super                  superelliptic_cech     superelliptic_drw_form superelliptic_witt    

 superelliptic          superelliptic_drw/     superelliptic_form     supersingular_D       

 superelliptic/         superelliptic_drw_cech superelliptic_function supersingular_j       [?7h[?12l[?25h[?25l[?7lelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7l

 super                 





 <unknown> [?7h[?12l[?25h[?25l[?7lelliptic

 super                 

 superelliptic         [?7h[?12l[?25h[?25l[?7l_drw/



 superelliptic          superelliptic_drw/    [?7h[?12l[?25h[?25l[?7la







[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltomorphism.sage[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/automorphism.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom(eta2)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2)

[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
[?7h([(1/(x^2 + 2*x))*y] d[x] + V(((-x^10 - x^7 - x^4 - x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(x/(x^2 + x + 1))*y]), [(2/(x + 1))*y], [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^14 - x^13 + x^11 + x^10 - x^7 + x^6 + x^4 + x^2 - x)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2)[?7h[?12l[?25h[?25l[?7l().coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2).coordinates()

[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 autom(eta2).coordinates()

File <string>:63, in coordinates(self, basis)

File <string>:81, in coordinates(self)

File <string>:87, in coordinates(self)

File <string>:87, in coordinates(self)

    [... skipping similar frames: coordinates at line 87 (64 times)]

File <string>:87, in coordinates(self)

File <string>:52, in coordinates(self)

File <string>:102, in degrees_de_rham0(self)

File <string>:80, in basis_de_rham_degrees(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File <string>:245, in reduction_form(C, g)

File <string>:222, in reduction(C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
    629     except KeyError:
    630         raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
    634 # At this point, we have only handled the "names" keyword if it was
    635 # needed. Since we know the variable names, it would logically be
    636 # an error to specify an additional "names" keyword. However,
   (...)
    639 # and we allow this for historical reasons. However, the names
    640 # must be consistent!
    641 if "names" in kwds:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2).coordinates()[?7h[?12l[?25h[?25l[?7l = C.de_rham_bass()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = autom(eta1)

[?7h[?12l[?25h[?2004l([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])) drw cech
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]) drw form
((-x^5 + x^3 + x)/(x^2*y - y)) dx form
(x/(x^2 + 2))*y function
(1/(x^3 + 2*x))*y function
V(1/x*y) witt
0 function
1/x*y function
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = autom(eta1)[?7h[?12l[?25h[?25l[?7l.coordinates([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: a.coordinates()

[?7h[?12l[?25h[?2004l(1, 0)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
aux V(smth) (V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 a.coordinates()

File <string>:75, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llimit = 10[?7h[?12l[?25h[?25l[?7load('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/automorphism.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ qui]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lell = [89, 983, 839, 43, 31, 167, 103, 40829, 653, 11969][?7h[?12l[?25h[?25l[?7lta2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lsage: eta2 - aux

[?7h[?12l[?25h[?2004l[?7h(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2 - aux)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7l().omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lomega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lsage: (eta2 - aux).omega0.omega.cartier()

[?7h[?12l[?25h[?2004l[?7h((-x^3)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lta2 - aux[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1.is_regular()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta1.r()

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2 - aux[?7h[?12l[?25h[?25l[?7l.omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:22, in <module>

File <string>:29, in de_rham_witt_lift(cech_class, prec)

File <string>:74, in __sub__(self, other)

File <string>:81, in __add__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'h1'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 

([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 

dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.coordinates()[?7h[?12l[?25h[?25l[?7lutm(eta2).coordinates()[?7h[?12l[?25h[?25l[?7lx.reduce()[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7hdV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.reduce()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.frobenius(*)

[?7h[?12l[?25h[?2004l  Input In [13]
    aux.frobenius(*)
                   ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius(*)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: aux.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7h((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldelta = f.discriminant()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8(aux.h2)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(aux.h2)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux)

[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)*y, ((x^4 + x^2 + 1)/x^6)*y, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux)[1].expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + t^13 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8 - aux

[?7h[?12l[?25h[?2004l[?7hV(((-x^8 + x^6 - 1)/y) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8 - aux[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (eta2.omega8 - aux).frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux).frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (eta2.omega8 - aux).frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + t^8 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^2 + 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^8 + 2*t^16 + O(t^18)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux).frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lonvert_superfct_into_AS(a.f)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: compare

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [32], in <cell line: 1>()
----> 1 compare

NameError: name 'compare' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8 - aux[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta.omega8[?7h[?12l[?25h[?25l[?7leta.omega8[?7h[?12l[?25h[?25l[?7lsage: eta.omega8

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [34], in <cell line: 1>()
----> 1 eta.omega8

AttributeError: 'function' object has no attribute 'omega8'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta.omega8[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.omega8 - aux[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8

[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^2 + 1)/(x^2*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7limit = 10[?7h[?12l[?25h[?25l[?7lft_form_to_drw(a)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lift2.omega8.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux).frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: (lift2 - eta2)

[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (lift2 - eta2).omega8.frobenius()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2).omega8.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().omega8.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (lift2 - eta2).omega

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 (lift2 - eta2).omega

AttributeError: 'superelliptic_drw_cech' object has no attribute 'omega'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2).omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (lift2 - eta2).omega0.omega

[?7h[?12l[?25h[?2004l[?7h((x^8 - x^6 + 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1;3S[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift2.omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lfomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lfor i in range(10):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7leC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7loC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lnC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ldC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l_C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lpC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ltC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lhC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l(C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.de_rham_basis()[1].omega8)

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.de_rham_basis()[1].omega8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l./[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.y)

[?7h[?12l[?25h[?2004l[?7h1/x^2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.y)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(lista_l)[?7h[?12l[?25h[?25l[?7latchC).crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lxC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7ltC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7liC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lcC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lhC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lmC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7luC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lrC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l(C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l() C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^.teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l3.teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l(3).teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -(C.x^3).teichmuller()*C.y.teichmuller.diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 -(C.x**Integer(3)).teichmuller()*C.y.teichmuller.diffn()

AttributeError: 'function' object has no attribute 'diffn'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3).teichmuller()*C.y.teichmuller.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -(C.x^3).teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(2*x^2/(x^2 + 2))*y] d[x] + V(((x^16 - x^12 - x^10)/(x^2*y - y)) dx) + dV([(2*x^12/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3).teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ltdifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lidifn()[?7h[?12l[?25h[?25l[?7lcdifn()[?7h[?12l[?25h[?25l[?7lhdifn()[?7h[?12l[?25h[?25l[?7lmdifn()[?7h[?12l[?25h[?25l[?7ludifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lrdifn()[?7h[?12l[?25h[?25l[?7l(difn()[?7h[?12l[?25h[?25l[?7l()difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -(C.x^3).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[((2*x^6 + 2*x^2 + 1)/(x^6 + 2*x^4))*y] d[x] + V(((x^24 - x^20 - x^18 + x^14 - x^12 + x^10 + x^8 - x^6 - 1)/(x^10*y - x^8*y)) dx) + dV([(2*x^12/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift2.omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: lift == omega8_lift

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift == omega8_lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l omega8_lift[?7h[?12l[?25h[?25l[?7l omega8_lift[?7h[?12l[?25h[?25l[?7l- omega8_lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lift - omega8_lift

[?7h[?12l[?25h[?2004l[?7h[((x^4 + x^2 + 1)/x^4)*y] d[x] + V(((-x^22 - x^20 + x^16 + x^14 + x^12 - x^10 - x^8 - x^6 - x^4 - x^2 + 1)/(x^8*y)) dx) + dV([((x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift - omega8_lift[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lift.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom3.reduce()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le3[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift([?7h[?12l[?25h[?25l[?7l_lift([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift.r()

[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^2 + 1)/(x^3*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift.r()[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift.r() ((-1)/(x*y)) dx
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift.r()[?7h[?12l[?25h[?25l[?7lft.r()[?7h[?12l[?25h[?25l[?7lsage: lift.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega8_lift.r()[?7h[?12l[?25h[?25l[?7lga8_lift.r()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift.r()

[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^2 + 1)/(x^3*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift.r()[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift.r() ((-1)/(x*y)) dx
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - omega8_lift

[?7h[?12l[?25h[?2004l[?7h[((x^4 + x^2 + 1)/x^4)*y] d[x] + V(((-x^22 - x^20 + x^16 + x^14 + x^12 - x^10 - x^8 - x^6 - x^4 - x^2 + 1)/(x^8*y)) dx) + dV([((x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7ldifn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l()*C.x.difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7ldifn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l()*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7lsage: -(C.x^3)*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^2 + 1)/(x^3*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3)*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(3)*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l-3)*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7lsage: -(C.x^(-3))*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^(-3))*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift.r() ((-1)/(x*y)) dx
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - omega8_lift[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga8_lift0 - omega8_lift[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - omega8_lift

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller.diffn().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn().r()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lus() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn().frobenius()

[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lyC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7ltC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7liC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lcC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lhC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lmC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7luC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lrC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l() C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2C.y.teichmuler() * C.y.teichmuler().difn() =[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler() * C.y.teichmuler().difn() =[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.teichmuler()[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l,).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l/).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l-).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y.teichmuller() * C.y.teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift.r()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_form_to_drw(a)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - omega8_lift[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0

[?7h[?12l[?25h[?2004l[?7h[2/x*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.diffn()

[?7h[?12l[?25h[?2004l[?7h[((x^2 + 1)/(x^4 + 2*x^2))*y] d[x] + V(((x^6 + 1)/(x^4*y - x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2).omega0.omega[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y.teichmuller() * C.y.teichmuller().diffn() == (C.x^3 - 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2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*(C.x.teichmuller())^(-2) * C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [34], in <cell line: 1>()
----> 1 Integer(2)*((C.x)**(-Integer(1))).teichmuller()*C.y.teichmuller().diffn() - Integer(2)*C.y.teichmuller()*(C.x.teichmuller())**(-Integer(2)) * C.x.teichmuller().diffn()

File /ext/sage/9.7/src/sage/rings/integer.pyx:2195, in sage.rings.integer.Integer.__pow__()
   2193         return coercion_model.bin_op(left, right, operator.pow)
   2194     # left is a non-Element: do the powering with a Python int
-> 2195     return left ** int(right)
   2196 
   2197 cpdef _pow_(self, other):

TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_witt' and 'int'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*(C.x.teichmuller())^(-2) * C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l( * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()).teichmuller())* Cx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l-)).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l1)).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[((x^3 + 2*x + 2)/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 - x^4 - x^3 - x^2 - x - 1)/(x*y)) dx) + dV([(2/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn()[?7h[?12l[?25h[?25l[?7lsage: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn() == omega8_lift0.diffn()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn() == omega8_lift0.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() - 2*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()

[?7h[?12l[?25h[?2004l[?7h((x^3 - x - 1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.diffn().r()

[?7h[?12l[?25h[?2004l[?7h((x^2 + 1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la8_lift0.diffn().r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0

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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.diffn().r()[?7h[?12l[?25h[?25l[?7l(2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * 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- 2*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)).teichmuler()*C.y.teichmuler().difn() - 2*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l+C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7lsage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()

[?7h[?12l[?25h[?2004l[?7h((x^3 - x + 1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.diffn().r()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.diffn().r() == (-C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r() == (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.yteichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l== (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)).teichmuler() * C.x.teichmuler().difn().r() = (-C.y/C.x).difn()[?7h[?12l[?25h[?25l[?7l2)).teichmuler() * C.x.teichmuler().difn().r() = (-C.y/C.x).difn()[?7h[?12l[?25h[?25l[?7lsage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-((C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x^(-2).teichmuler() * C.x.teichmuler().difn()).r() = (-C.y/C.x).difn()
[?7h[?12l[?25h[?25l[?7lsage: -(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()


[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()
[?7h[?12l[?25h[?25l[?7l
([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: -(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r()

[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: (-C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?7h((x^2 + 1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: (-C.y/C.x).diffn() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lt*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7li*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lc*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lh*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lm*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lu*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lr*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l(*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.x)^(-1).teichmuler()*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).teichmuler()*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ledifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lidifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lcdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lhdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lmdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ludifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lldifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lldifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ledifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lrdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l(difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l().difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lt*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7li*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lc*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lh*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lm*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lu*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lr*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l(*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().*C.dx[?7h[?12l[?25h[?25l[?7lt*C.dx[?7h[?12l[?25h[?25l[?7le*C.dx[?7h[?12l[?25h[?25l[?7li*C.dx[?7h[?12l[?25h[?25l[?7lc*C.dx[?7h[?12l[?25h[?25l[?7lh*C.dx[?7h[?12l[?25h[?25l[?7lm*C.dx[?7h[?12l[?25h[?25l[?7lu*C.dx[?7h[?12l[?25h[?25l[?7ll*C.dx[?7h[?12l[?25h[?25l[?7ll*C.dx[?7h[?12l[?25h[?25l[?7le*C.dx[?7h[?12l[?25h[?25l[?7lr*C.dx[?7h[?12l[?25h[?25l[?7l(*C.dx[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7l(())*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la-(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l -(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=-(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l -(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: a = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)^(-2).teichmuller())*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [48], in <cell line: 1>()
----> 1 a = -((C.x)**(-Integer(1))).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)**(-Integer(2)).teichmuller())*C.x.teichmuller().diffn()

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'teichmuller'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)^(-2).teichmuller())*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: a = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*(((C.x)^(-2)).teichmuller())*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*(((C.x)^(-2)).teichmuller())*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lsage: a.r() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.r() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l = -((C.x)^(-1)).teichmuller()*C.y.teichmuller(.diffn() + C.y.teichmuller()*(((C.x)^(-2)).teichmuller())*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.x)^(-2).teichmuller())*C.xteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-C.y/C.x).diffn() == -(C.x)^-1)*Cy.diffn() + Cy*(C.x^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7l() == (-C.y/C.x).diffn()
[?7h[?12l[?25h[?25l[?7l
(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x^(-2).teichmuler() * C.x.teichmuler().difn().r() = (-C.y/C.x).difn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r() == (-Cy/C.x).diffn()[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.yteichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r() == (-Cy/C.x).diffn()[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.yteichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.diffn().r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - omega8_lift[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - omega8_lift[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - a

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 omega8_lift0 - a

File <string>:35, in __sub__(self, other)

File <string>:29, in __add__(self, other)

AttributeError: 'superelliptic_drw_form' object has no attribute 't'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - a[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0

[?7h[?12l[?25h[?2004l[?7h[2/x*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l - a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. - a[?7h[?12l[?25h[?25l[?7ld - a[?7h[?12l[?25h[?25l[?7li - a[?7h[?12l[?25h[?25l[?7lf - a[?7h[?12l[?25h[?25l[?7lf - a[?7h[?12l[?25h[?25l[?7ln - a[?7h[?12l[?25h[?25l[?7l( - a[?7h[?12l[?25h[?25l[?7l() - a[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.diffn() - a

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpare[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: compare

[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: compare.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare.r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: compare.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^2 + 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: compare.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^8 + 2*t^16 + O(t^18)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn() - a[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: omega0_lift0

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [59], in <cell line: 1>()
----> 1 omega0_lift0

NameError: name 'omega0_lift0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0_lift0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_lift0[?7h[?12l[?25h[?25l[?7l8_lift0[?7h[?12l[?25h[?25l[?7l.diffn() - a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l - a[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - compare

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 omega8_lift0 - compare

File <string>:39, in __sub__(self, other)

AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. - compare[?7h[?12l[?25h[?25l[?7lo - compare[?7h[?12l[?25h[?25l[?7lm - compare[?7h[?12l[?25h[?25l[?7le - compare[?7h[?12l[?25h[?25l[?7lg - compare[?7h[?12l[?25h[?25l[?7la - compare[?7h[?12l[?25h[?25l[?7l8 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.omega8 - compare

[?7h[?12l[?25h[?2004l[?7hdV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:22, in <module>

File <string>:30, in de_rham_witt_lift(cech_class, prec)

File <string>:74, in __sub__(self, other)

File <string>:81, in __add__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'h1'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: False
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
 
 [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
 
 0 
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: False
test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test0: True
test: False
test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [69], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:22, in <module>

File <string>:33, in de_rham_witt_lift(cech_class, prec)

File <string>:29, in __add__(self, other)

AttributeError: 'superelliptic_drw_form' object has no attribute 't'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: False
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
test 3: False False True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:22, in <module>

File <string>:28, in de_rham_witt_lift(cech_class, prec)

File <string>:29, in __add__(self, other)

AttributeError: 'superelliptic_drw_form' object has no attribute 't'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
test 3: True True True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
test 3: True True True
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:24, in <module>

NameError: name 'aux' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.r() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lux.r()[?7h[?12l[?25h[?25l[?7ltometa2).coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7leta2lift[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbautom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7lautom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l=autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift) - eta2lift

[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((x^4 + x^2 - 1)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7lsage: b

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^4)/(x^3*y - x^2*y - x*y + y)) dx) + dV([((x^2 + 1)/(x^3 + 2*x^2 + 2*x + 1))*y]), [(1/(x^2 + x))*y] + V(((x + 2)/(x^2 + x))*y), [(1/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 - x^7 + x^2 - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((x^3 + 2*x^2 + 2*x + 2)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.r()

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.r()[?7h[?12l[?25h[?25l[?7l = autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: b - eta1

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 b - eta1

NameError: name 'eta1' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_witt_lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de

 C.de_rham_basis                     C.degrees_de_rham1                 

 C.degrees_de_rham0                  C.degrees_holomorphic_differentials





 [?7h[?12l[?25h[?25l[?7l_rham_basis

 C.de_rham_basis                    



 <unknown> [?7h[?12l[?25h[?25l[?7l[





[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de_rham_basis[0])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 eta1 = de_rham_witt_lift(C.de_rham_basis[Integer(0)])

TypeError: 'method' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = de_rham_witt_lift(C.de_rham_basis[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0])[?7h[?12l[?25h[?25l[?7l)[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de_rham_basis()[0])

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = de_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = de_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l[0])[?7h[?12l[?25h[?25l[?7lb - eta1[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift) - eta2lift - eta1

[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((x^4 + x^2 - 1)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.omega0.frobenius()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.omega0.frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7l8.frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b.omega8.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 - 1)/(x^4*y - x^3*y + x^2*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.omega8.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.omega8.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^2 + t^10 + O(t^12)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laeta2lift[?7h[?12l[?25h[?25l[?7lueta2lift[?7h[?12l[?25h[?25l[?7lteta2lift[?7h[?12l[?25h[?25l[?7loeta2lift[?7h[?12l[?25h[?25l[?7lmeta2lift[?7h[?12l[?25h[?25l[?7l(eta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2lift).coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 autom(eta2lift).coordinates()

File <string>:63, in coordinates(self, basis)

File <string>:81, in coordinates(self)

File <string>:87, in coordinates(self)

File <string>:87, in coordinates(self)

    [... skipping similar frames: coordinates at line 87 (686 times)]

File <string>:87, in coordinates(self)

File <string>:52, in coordinates(self)

File <string>:102, in degrees_de_rham0(self)

File <string>:76, in basis_de_rham_degrees(self)

File <string>:60, in holomorphic_differentials_basis(self)

File <string>:52, in basis_holomorphic_differentials_degree(self)

File <string>:7, in __init__(self, C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
    704 x0, y0 = x, y
    705 try:
--> 706     x, y = resolve_fractions(x0, y0)
    707 except (AttributeError, TypeError):
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))

File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
    686 yd = y.denominator()
    687 try:
--> 688     return (xn * yd, yn * xd)
    689 except (AttributeError, TypeError, ValueError):
    690     pass

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1198 # Now coerce to a common parent and do the operation there
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:
   1202     self._record_exception()

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1313     x_elt = x
   1314 if y_map is not None:
-> 1315     y_elt = (<Map>y_map)._call_(y)
   1316 else:
   1317     y_elt = y

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:426, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    424         v.append(B(w))
    425         z *= var
--> 426     return ring(v)
    427 
    428 cpdef dict _mpoly_dict_recursive(self, tuple vars=None, base_ring=None):

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:416, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    414 C = self.element_class
    415 if isinstance(x, (list, tuple)):
--> 416     return C(self, x, check=check, is_gen=False, construct=construct)
    417 if isinstance(x, range):
    418     return C(self, list(x), check=check, is_gen=False,
    419              construct=construct)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2lift).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm(eta2lift).coordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2lift)

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([(x/(x^2 + x + 1))*y]), [(2/(x + 1))*y], [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 - x^2 + 1)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2lift)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbautom(eta2lift)[?7h[?12l[?25h[?25l[?7l autom(eta2lift)[?7h[?12l[?25h[?25l[?7l=autom(eta2lift)[?7h[?12l[?25h[?25l[?7l autom(eta2lift)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l() - eta2lift - eta1[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift) - eta2lift - eta1

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 b = autom(eta2lift) - eta2lift - eta1

File <string>:23, in autom(self)

File <string>:20, in autom(self)

File <string>:99, in diffn(self, dy_w)

File <string>:99, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:70, in __rmul__(self, constant)

File <string>:14, in __init__(self, C, g)

File <string>:223, in reduction(C, g)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift)[?7h[?12l[?25h[?25l[?7l.omega8.frobenus().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 b.coordinates()

File <string>:63, in coordinates(self, basis)

File <string>:81, in coordinates(self)

File <string>:87, in coordinates(self)

File <string>:87, in coordinates(self)

    [... skipping similar frames: coordinates at line 87 (328 times)]

File <string>:87, in coordinates(self)

File <string>:86, in coordinates(self)

File <string>:52, in __sub__(self, other)

File <string>:14, in __init__(self, C, g)

File <string>:216, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
    704 x0, y0 = x, y
    705 try:
--> 706     x, y = resolve_fractions(x0, y0)
    707 except (AttributeError, TypeError):
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.r()

[?7h[?12l[?25h[?2004l[?7h(((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.r()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.r().coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 b.r().coordinates()

File <string>:81, in coordinates(self)

File <string>:87, in coordinates(self)

File <string>:87, in coordinates(self)

    [... skipping similar frames: coordinates at line 87 (295 times)]

File <string>:87, in coordinates(self)

File <string>:56, in coordinates(self)

File <string>:98, in de_rham_basis(self)

File <string>:76, in basis_de_rham_degrees(self)

File <string>:60, in holomorphic_differentials_basis(self)

File <string>:52, in basis_holomorphic_differentials_degree(self)

File <string>:7, in __init__(self, C, g)

File <string>:256, in reduction_form(C, g)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [21], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

TypeError: 'method' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

AttributeError: 'NoneType' object has no attribute 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2lift)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:16, in autom(self)

TypeError: superelliptic_cech.__init__() missing 1 required positional argument: 'fct'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
self ((1/y) dx, (2/(x^3 + x^2))*y, ((x^2 + x + 1)/(x^2*y + x*y)) dx)
self ((1/y) dx, (1/(x^4 + x^3))*y, ((x^4 + x^3 + x^2 - x - 1)/(x^4*y + x^3*y)) dx)
self ((1/y) dx, (2/(x^5 + x^4))*y, ((x^5 + x^4 + x^2 + x - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (1/(x^6 + x^5))*y, ((x^5 + x^4 - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (2/(x^7 + x^6))*y, ((x^7 + x^6 - x^2 + x + 1)/(x^7*y + x^6*y)) dx)
self ((1/y) dx, (1/(x^8 + x^7))*y, ((x^8 + x^7 - x^2 - x + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (2/(x^9 + x^8))*y, ((x^8 + x^7 + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (1/(x^10 + x^9))*y, ((x^10 + x^9 + x^2 - x - 1)/(x^10*y + x^9*y)) dx)
self ((1/y) dx, (2/(x^11 + x^10))*y, ((x^11 + x^10 + x^2 + x - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (1/(x^12 + x^11))*y, ((x^11 + x^10 - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (2/(x^13 + x^12))*y, ((x^13 + x^12 - x^2 + x + 1)/(x^13*y + x^12*y)) dx)
self ((1/y) dx, (1/(x^14 + x^13))*y, ((x^14 + x^13 - x^2 - x + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (2/(x^15 + x^14))*y, ((x^14 + x^13 + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (1/(x^16 + x^15))*y, ((x^16 + x^15 + x^2 - x - 1)/(x^16*y + x^15*y)) dx)
self ((1/y) dx, (2/(x^17 + x^16))*y, ((x^17 + x^16 + x^2 + x - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (1/(x^18 + x^17))*y, ((x^17 + x^16 - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (2/(x^19 + x^18))*y, ((x^19 + x^18 - x^2 + x + 1)/(x^19*y + x^18*y)) dx)
self ((1/y) dx, (1/(x^20 + x^19))*y, ((x^20 + x^19 - x^2 - x + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (2/(x^21 + x^20))*y, ((x^20 + x^19 + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (1/(x^22 + x^21))*y, ((x^22 + x^21 + x^2 - x - 1)/(x^22*y + x^21*y)) dx)
self ((1/y) dx, (2/(x^23 + x^22))*y, ((x^23 + x^22 + x^2 + x - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (1/(x^24 + x^23))*y, ((x^23 + x^22 - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (2/(x^25 + x^24))*y, ((x^25 + x^24 - x^2 + x + 1)/(x^25*y + x^24*y)) dx)
self ((1/y) dx, (1/(x^26 + x^25))*y, ((x^26 + x^25 - x^2 - x + 1)/(x^26*y + x^25*y)) dx)
self ((1/y) dx, (2/(x^27 + x^26))*y, ((x^26 + x^25 + 1)/(x^26*y + x^25*y)) dx)
self ((1/y) dx, (1/(x^28 + x^27))*y, ((x^28 + x^27 + x^2 - x - 1)/(x^28*y + x^27*y)) dx)
self ((1/y) dx, (2/(x^29 + x^28))*y, ((x^29 + x^28 + x^2 + x - 1)/(x^29*y + x^28*y)) dx)
self ((1/y) dx, (1/(x^30 + x^29))*y, ((x^29 + x^28 - 1)/(x^29*y + x^28*y)) dx)
self ((1/y) dx, (2/(x^31 + x^30))*y, ((x^31 + x^30 - x^2 + x + 1)/(x^31*y + x^30*y)) dx)
self ((1/y) dx, (1/(x^32 + x^31))*y, ((x^32 + x^31 - x^2 - x + 1)/(x^32*y + x^31*y)) dx)
self ((1/y) dx, (2/(x^33 + x^32))*y, ((x^32 + x^31 + 1)/(x^32*y + x^31*y)) dx)
self ((1/y) dx, (1/(x^34 + x^33))*y, ((x^34 + x^33 + x^2 - x - 1)/(x^34*y + x^33*y)) dx)
self ((1/y) dx, (2/(x^35 + x^34))*y, ((x^35 + x^34 + x^2 + x - 1)/(x^35*y + x^34*y)) dx)
self ((1/y) dx, (1/(x^36 + x^35))*y, ((x^35 + x^34 - 1)/(x^35*y + x^34*y)) dx)
self ((1/y) dx, (2/(x^37 + x^36))*y, ((x^37 + x^36 - x^2 + x + 1)/(x^37*y + x^36*y)) dx)
self ((1/y) dx, (1/(x^38 + x^37))*y, ((x^38 + x^37 - x^2 - x + 1)/(x^38*y + x^37*y)) dx)
self ((1/y) dx, (2/(x^39 + x^38))*y, ((x^38 + x^37 + 1)/(x^38*y + x^37*y)) dx)
self ((1/y) dx, (1/(x^40 + x^39))*y, ((x^40 + x^39 + x^2 - x - 1)/(x^40*y + x^39*y)) dx)
self ((1/y) dx, (2/(x^41 + x^40))*y, ((x^41 + x^40 + x^2 + x - 1)/(x^41*y + x^40*y)) dx)
self ((1/y) dx, (1/(x^42 + x^41))*y, ((x^41 + x^40 - 1)/(x^41*y + x^40*y)) dx)
self ((1/y) dx, (2/(x^43 + x^42))*y, ((x^43 + x^42 - x^2 + x + 1)/(x^43*y + x^42*y)) dx)
self ((1/y) dx, (1/(x^44 + x^43))*y, ((x^44 + x^43 - x^2 - x + 1)/(x^44*y + x^43*y)) dx)
self ((1/y) dx, (2/(x^45 + x^44))*y, ((x^44 + x^43 + 1)/(x^44*y + x^43*y)) dx)
self ((1/y) dx, (1/(x^46 + x^45))*y, ((x^46 + x^45 + x^2 - x - 1)/(x^46*y + x^45*y)) dx)
self ((1/y) dx, (2/(x^47 + x^46))*y, ((x^47 + x^46 + x^2 + x - 1)/(x^47*y + x^46*y)) dx)
self ((1/y) dx, (1/(x^48 + x^47))*y, ((x^47 + x^46 - 1)/(x^47*y + x^46*y)) dx)
self ((1/y) dx, (2/(x^49 + x^48))*y, ((x^49 + x^48 - x^2 + x + 1)/(x^49*y + x^48*y)) dx)
self ((1/y) dx, (1/(x^50 + x^49))*y, ((x^50 + x^49 - x^2 - x + 1)/(x^50*y + x^49*y)) dx)
self ((1/y) dx, (2/(x^51 + x^50))*y, ((x^50 + x^49 + 1)/(x^50*y + x^49*y)) dx)
self ((1/y) dx, (1/(x^52 + x^51))*y, ((x^52 + x^51 + x^2 - x - 1)/(x^52*y + x^51*y)) dx)
self ((1/y) dx, (2/(x^53 + x^52))*y, ((x^53 + x^52 + x^2 + x - 1)/(x^53*y + x^52*y)) dx)
self ((1/y) dx, (1/(x^54 + x^53))*y, ((x^53 + x^52 - 1)/(x^53*y + x^52*y)) dx)
self ((1/y) dx, (2/(x^55 + x^54))*y, ((x^55 + x^54 - x^2 + x + 1)/(x^55*y + x^54*y)) dx)
self ((1/y) dx, (1/(x^56 + x^55))*y, ((x^56 + x^55 - x^2 - x + 1)/(x^56*y + x^55*y)) dx)
self ((1/y) dx, (2/(x^57 + x^56))*y, ((x^56 + x^55 + 1)/(x^56*y + x^55*y)) dx)
self ((1/y) dx, (1/(x^58 + x^57))*y, ((x^58 + x^57 + x^2 - x - 1)/(x^58*y + x^57*y)) dx)
self ((1/y) dx, (2/(x^59 + x^58))*y, ((x^59 + x^58 + x^2 + x - 1)/(x^59*y + x^58*y)) dx)
self ((1/y) dx, (1/(x^60 + x^59))*y, ((x^59 + x^58 - 1)/(x^59*y + x^58*y)) dx)
self ((1/y) dx, (2/(x^61 + x^60))*y, ((x^61 + x^60 - x^2 + x + 1)/(x^61*y + x^60*y)) dx)
self ((1/y) dx, (1/(x^62 + x^61))*y, ((x^62 + x^61 - x^2 - x + 1)/(x^62*y + x^61*y)) dx)
self ((1/y) dx, (2/(x^63 + x^62))*y, ((x^62 + x^61 + 1)/(x^62*y + x^61*y)) dx)
self ((1/y) dx, (1/(x^64 + x^63))*y, ((x^64 + x^63 + x^2 - x - 1)/(x^64*y + x^63*y)) dx)
self ((1/y) dx, (2/(x^65 + x^64))*y, ((x^65 + x^64 + x^2 + x - 1)/(x^65*y + x^64*y)) dx)
self ((1/y) dx, (1/(x^66 + x^65))*y, ((x^65 + x^64 - 1)/(x^65*y + x^64*y)) dx)
self ((1/y) dx, (2/(x^67 + x^66))*y, ((x^67 + x^66 - x^2 + x + 1)/(x^67*y + x^66*y)) dx)
self ((1/y) dx, (1/(x^68 + x^67))*y, ((x^68 + x^67 - x^2 - x + 1)/(x^68*y + x^67*y)) dx)
self ((1/y) dx, (2/(x^69 + x^68))*y, ((x^68 + x^67 + 1)/(x^68*y + x^67*y)) dx)
self ((1/y) dx, (1/(x^70 + x^69))*y, ((x^70 + x^69 + x^2 - x - 1)/(x^70*y + x^69*y)) dx)
self ((1/y) dx, (2/(x^71 + x^70))*y, ((x^71 + x^70 + x^2 + x - 1)/(x^71*y + x^70*y)) dx)
self ((1/y) dx, (1/(x^72 + x^71))*y, ((x^71 + x^70 - 1)/(x^71*y + x^70*y)) dx)
self ((1/y) dx, (2/(x^73 + x^72))*y, ((x^73 + x^72 - x^2 + x + 1)/(x^73*y + x^72*y)) dx)
self ((1/y) dx, (1/(x^74 + x^73))*y, ((x^74 + x^73 - x^2 - x + 1)/(x^74*y + x^73*y)) dx)
self ((1/y) dx, (2/(x^75 + x^74))*y, ((x^74 + x^73 + 1)/(x^74*y + x^73*y)) dx)
self ((1/y) dx, (1/(x^76 + x^75))*y, ((x^76 + x^75 + x^2 - x - 1)/(x^76*y + x^75*y)) dx)
self ((1/y) dx, (2/(x^77 + x^76))*y, ((x^77 + x^76 + x^2 + x - 1)/(x^77*y + x^76*y)) dx)
self ((1/y) dx, (1/(x^78 + x^77))*y, ((x^77 + x^76 - 1)/(x^77*y + x^76*y)) dx)
self ((1/y) dx, (2/(x^79 + x^78))*y, ((x^79 + x^78 - x^2 + x + 1)/(x^79*y + x^78*y)) dx)
self ((1/y) dx, (1/(x^80 + x^79))*y, ((x^80 + x^79 - x^2 - x + 1)/(x^80*y + x^79*y)) dx)
self ((1/y) dx, (2/(x^81 + x^80))*y, ((x^80 + x^79 + 1)/(x^80*y + x^79*y)) dx)
self ((1/y) dx, (1/(x^82 + x^81))*y, ((x^82 + x^81 + x^2 - x - 1)/(x^82*y + x^81*y)) dx)
self ((1/y) dx, (2/(x^83 + x^82))*y, ((x^83 + x^82 + x^2 + x - 1)/(x^83*y + x^82*y)) dx)
self ((1/y) dx, (1/(x^84 + x^83))*y, ((x^83 + x^82 - 1)/(x^83*y + x^82*y)) dx)
self ((1/y) dx, (2/(x^85 + x^84))*y, ((x^85 + x^84 - x^2 + x + 1)/(x^85*y + x^84*y)) dx)
self ((1/y) dx, (1/(x^86 + x^85))*y, ((x^86 + x^85 - x^2 - x + 1)/(x^86*y + x^85*y)) dx)
self ((1/y) dx, (2/(x^87 + x^86))*y, ((x^86 + x^85 + 1)/(x^86*y + x^85*y)) dx)
self ((1/y) dx, (1/(x^88 + x^87))*y, ((x^88 + x^87 + x^2 - x - 1)/(x^88*y + x^87*y)) dx)
self ((1/y) dx, (2/(x^89 + x^88))*y, ((x^89 + x^88 + x^2 + x - 1)/(x^89*y + x^88*y)) dx)
self ((1/y) dx, (1/(x^90 + x^89))*y, ((x^89 + x^88 - 1)/(x^89*y + x^88*y)) dx)
self ((1/y) dx, (2/(x^91 + x^90))*y, ((x^91 + x^90 - x^2 + x + 1)/(x^91*y + x^90*y)) dx)
self ((1/y) dx, (1/(x^92 + x^91))*y, ((x^92 + x^91 - x^2 - x + 1)/(x^92*y + x^91*y)) dx)
self ((1/y) dx, (2/(x^93 + x^92))*y, ((x^92 + x^91 + 1)/(x^92*y + x^91*y)) dx)
self ((1/y) dx, (1/(x^94 + x^93))*y, ((x^94 + x^93 + x^2 - x - 1)/(x^94*y + x^93*y)) dx)
self ((1/y) dx, (2/(x^95 + x^94))*y, ((x^95 + x^94 + x^2 + x - 1)/(x^95*y + x^94*y)) dx)
self ((1/y) dx, (1/(x^96 + x^95))*y, ((x^95 + x^94 - 1)/(x^95*y + x^94*y)) dx)
self ((1/y) dx, (2/(x^97 + x^96))*y, ((x^97 + x^96 - x^2 + x + 1)/(x^97*y + x^96*y)) dx)
self ((1/y) dx, (1/(x^98 + x^97))*y, ((x^98 + x^97 - x^2 - x + 1)/(x^98*y + x^97*y)) dx)
self ((1/y) dx, (2/(x^99 + x^98))*y, ((x^98 + x^97 + 1)/(x^98*y + x^97*y)) dx)
self ((1/y) dx, (1/(x^100 + x^99))*y, ((x^100 + x^99 + x^2 - x - 1)/(x^100*y + x^99*y)) dx)
self ((1/y) dx, (2/(x^101 + x^100))*y, ((x^101 + x^100 + x^2 + x - 1)/(x^101*y + x^100*y)) dx)
self ((1/y) dx, (1/(x^102 + x^101))*y, ((x^101 + x^100 - 1)/(x^101*y + x^100*y)) dx)
self ((1/y) dx, (2/(x^103 + x^102))*y, ((x^103 + x^102 - x^2 + x + 1)/(x^103*y + x^102*y)) dx)
self ((1/y) dx, (1/(x^104 + x^103))*y, ((x^104 + x^103 - x^2 - x + 1)/(x^104*y + x^103*y)) dx)
self ((1/y) dx, (2/(x^105 + x^104))*y, ((x^104 + x^103 + 1)/(x^104*y + x^103*y)) dx)
self ((1/y) dx, (1/(x^106 + x^105))*y, ((x^106 + x^105 + x^2 - x - 1)/(x^106*y + x^105*y)) dx)
self ((1/y) dx, (2/(x^107 + x^106))*y, ((x^107 + x^106 + x^2 + x - 1)/(x^107*y + x^106*y)) dx)
self ((1/y) dx, (1/(x^108 + x^107))*y, ((x^107 + x^106 - 1)/(x^107*y + x^106*y)) dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:82, in coordinates(self)

File <string>:88, in coordinates(self)

File <string>:88, in coordinates(self)

    [... skipping similar frames: coordinates at line 88 (103 times)]

File <string>:88, in coordinates(self)

File <string>:53, in coordinates(self)

File <string>:102, in degrees_de_rham0(self)

File <string>:76, in basis_de_rham_degrees(self)

File <string>:60, in holomorphic_differentials_basis(self)

File <string>:52, in basis_holomorphic_differentials_degree(self)

File <string>:7, in __init__(self, C, g)

File <string>:259, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))
    710 try:
--> 711     return self._element_class(self, x, y, coerce=coerce)
    712 except TypeError:
    713     if parent(x) is parent(x0):

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    113 if coerce:
    114     self.__numerator   = parent.ring()(numerator)
--> 115     self.__denominator = parent.ring()(denominator)
    116 else:
    117     self.__numerator   = numerator

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2667, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2665         else:
   2666             var = ""
-> 2667         s += "%s%s"%(x,var)
   2668 s = s.replace(" + -", " - ")
   2669 s = re.sub(r' 1(\.0+)?\*',' ', s)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
self ((1/y) dx, (2/(x^3 + x^2))*y, ((x^2 + x + 1)/(x^2*y + x*y)) dx)
self ((1/y) dx, (1/(x^4 + x^3))*y, ((x^4 + x^3 + x^2 - x - 1)/(x^4*y + x^3*y)) dx)
self ((1/y) dx, (2/(x^5 + x^4))*y, ((x^5 + x^4 + x^2 + x - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (1/(x^6 + x^5))*y, ((x^5 + x^4 - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (2/(x^7 + x^6))*y, ((x^7 + x^6 - x^2 + x + 1)/(x^7*y + x^6*y)) dx)
self ((1/y) dx, (1/(x^8 + x^7))*y, ((x^8 + x^7 - x^2 - x + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (2/(x^9 + x^8))*y, ((x^8 + x^7 + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (1/(x^10 + x^9))*y, ((x^10 + x^9 + x^2 - x - 1)/(x^10*y + x^9*y)) dx)
self ((1/y) dx, (2/(x^11 + x^10))*y, ((x^11 + x^10 + x^2 + x - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (1/(x^12 + x^11))*y, ((x^11 + x^10 - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (2/(x^13 + x^12))*y, ((x^13 + x^12 - x^2 + x + 1)/(x^13*y + x^12*y)) dx)
self ((1/y) dx, (1/(x^14 + x^13))*y, ((x^14 + x^13 - x^2 - x + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (2/(x^15 + x^14))*y, ((x^14 + x^13 + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (1/(x^16 + x^15))*y, ((x^16 + x^15 + x^2 - x - 1)/(x^16*y + x^15*y)) dx)
self ((1/y) dx, (2/(x^17 + x^16))*y, ((x^17 + x^16 + x^2 + x - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (1/(x^18 + x^17))*y, ((x^17 + x^16 - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (2/(x^19 + x^18))*y, ((x^19 + x^18 - x^2 + x + 1)/(x^19*y + x^18*y)) dx)
self ((1/y) dx, (1/(x^20 + x^19))*y, ((x^20 + x^19 - x^2 - x + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (2/(x^21 + x^20))*y, ((x^20 + x^19 + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (1/(x^22 + x^21))*y, ((x^22 + x^21 + x^2 - x - 1)/(x^22*y + x^21*y)) dx)
self ((1/y) dx, (2/(x^23 + x^22))*y, ((x^23 + x^22 + x^2 + x - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (1/(x^24 + x^23))*y, ((x^23 + x^22 - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (2/(x^25 + x^24))*y, ((x^25 + x^24 - x^2 + x + 1)/(x^25*y + x^24*y)) dx)
self ((1/y) dx, (1/(x^26 + x^25))*y, ((x^26 + x^25 - x^2 - x + 1)/(x^26*y + x^25*y)) dx)
self ((1/y) dx, (2/(x^27 + x^26))*y, ((x^26 + x^25 + 1)/(x^26*y + x^25*y)) dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:82, in coordinates(self)

File <string>:88, in coordinates(self)

File <string>:88, in coordinates(self)

    [... skipping similar frames: coordinates at line 88 (22 times)]

File <string>:88, in coordinates(self)

File <string>:57, in coordinates(self)

File <string>:98, in de_rham_basis(self)

File <string>:91, in basis_de_rham_degrees(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:93, in diffn(self)

File /ext/sage/9.7/src/sage/categories/quotient_fields.py:610, in QuotientFields.ElementMethods.derivative(self, *args)
    580 r"""
    581 The derivative of this rational function, with respect to variables
    582 supplied in args.
   (...)
    607     2/(x^3 + 3*x^2*y + 3*x*y^2 + y^3)
    608 """
    609 from sage.misc.derivative import multi_derivative
--> 610 return multi_derivative(self, args)

File /ext/sage/9.7/src/sage/misc/derivative.pyx:222, in sage.misc.derivative.multi_derivative()
    220 
    221     for arg in derivative_parse(args):
--> 222         F = F._derivative(arg)
    223     return F
    224 

File /ext/sage/9.7/src/sage/categories/quotient_fields.py:612, in QuotientFields.ElementMethods._derivative(self, var)
    609     from sage.misc.derivative import multi_derivative
    610     return multi_derivative(self, args)
--> 612 def _derivative(self, var=None):
    613     r"""
    614     Returns the derivative of this rational function with respect to the
    615     variable ``var``.
   (...)
    668         (-t + 1)/(t^3 + 3*t^2 + 3*t + 1)
    669     """
    670     R = self.parent()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(autom(C.de_rham_basis()[1]).coordinates())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.

  C.a_number                               C.cartier_matrix                         C.de_rham_basis                           

  C.base_ring                              C.characteristic                         C.degrees_de_rham0                        

  C.basis_de_rham_degrees                  C.cohomology_of_structure_sheaf_basis    C.degrees_de_rham1                       >

  C.basis_holomorphic_differentials_degree C.crystalline_cohomology_basis           C.degrees_holomorphic_differentials       

 [?7h[?12l[?25h[?25l[?7la_number

 C.a_number                              







 <unknown> [?7h[?12l[?25h[?25l[?7lcartier_matrix

 C.a_number                               C.cartier_matrix                        [?7h[?12l[?25h[?25l[?7lharacteristc

 C.cartier_matrix                        

 C.characteristic                        [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis



 C.characteristic                        

 C.cohomology_of_structure_sheaf_basis   [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?7h[2/x*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7luC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7ltC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7loC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7lmC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7l(C.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.cohomology_of_structure_sheaf_basis()[0]).coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = autm(b[0])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsperelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lerelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1, 2)[?7h[?12l[?25h[?25l[?7l7 + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^7 + 1, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 2)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((x/y) dx, 0, (x/y) dx),
 ((x^2/y) dx, 0, (x^2/y) dx),
 (((-x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
 (0 dx, 2/x^2*y, (1/(x^3*y)) dx),
 ((x^3/y) dx, 2/x^3*y, 0 dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?7h[2/x*y, 2/x^2*y, 2/x^3*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^7 + 1, 5)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?7h[2/x*y,
 2/x*y^2,
 2/x^2*y^2,
 2/x*y^3,
 2/x^2*y^3,
 2/x^3*y^3,
 2/x^4*y^3,
 2/x*y^4,
 2/x^2*y^4,
 2/x^3*y^4,
 2/x^4*y^4,
 2/x^5*y^4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^7 + 1, 5)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((1/y^2) dx, 0, (1/y^2) dx),
 ((x/y^2) dx, 0, (x/y^2) dx),
 ((1/y^3) dx, 0, (1/y^3) dx),
 ((x/y^3) dx, 0, (x/y^3) dx),
 ((x^2/y^3) dx, 0, (x^2/y^3) dx),
 ((x^3/y^3) dx, 0, (x^3/y^3) dx),
 ((1/y^4) dx, 0, (1/y^4) dx),
 ((x/y^4) dx, 0, (x/y^4) dx),
 ((x^2/y^4) dx, 0, (x^2/y^4) dx),
 ((x^3/y^4) dx, 0, (x^3/y^4) dx),
 ((x^4/y^4) dx, 0, (x^4/y^4) dx),
 (((-x^5)/y) dx, 2/x*y^4, ((-1)/(x^2*y)) dx),
 (0 dx, 2/x^2*y^4, (1/(x^3*y)) dx),
 ((x^3/y) dx, 2/x^3*y^4, 0 dx),
 (((-x^2)/y) dx, 2/x^4*y^4, ((-1)/(x^5*y)) dx),
 (0 dx, 2/x^5*y^4, (1/(x^6*y)) dx),
 ((x^5/y^2) dx, 2/x*y^3, ((-1)/(x^2*y^2)) dx),
 (((-x^4)/y^2) dx, 2/x^2*y^3, (1/(x^3*y^2)) dx),
 (0 dx, 2/x^3*y^3, 0 dx),
 ((x^2/y^2) dx, 2/x^4*y^3, ((-1)/(x^5*y^2)) dx),
 (0 dx, 2/x*y^2, ((-1)/(x^2*y^3)) dx),
 ((x^4/y^3) dx, 2/x^2*y^2, (1/(x^3*y^3)) dx),
 (((-x^5)/y^4) dx, 2/x*y, ((-1)/(x^2*y^4)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.de_rham_basis([?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^7 + 1, 5)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((1/y^2) dx, 0, (1/y^2) dx),
 ((x/y^2) dx, 0, (x/y^2) dx),
 ((1/y^3) dx, 0, (1/y^3) dx),
 ((x/y^3) dx, 0, (x/y^3) dx),
 ((x^2/y^3) dx, 0, (x^2/y^3) dx),
 ((x^3/y^3) dx, 0, (x^3/y^3) dx),
 ((1/y^4) dx, 0, (1/y^4) dx),
 ((x/y^4) dx, 0, (x/y^4) dx),
 ((x^2/y^4) dx, 0, (x^2/y^4) dx),
 ((x^3/y^4) dx, 0, (x^3/y^4) dx),
 ((x^4/y^4) dx, 0, (x^4/y^4) dx),
 (((-x^5)/y) dx, 2/x*y^4, ((-1)/(x^2*y)) dx),
 (0 dx, 2/x^2*y^4, (1/(x^3*y)) dx),
 ((x^3/y) dx, 2/x^3*y^4, 0 dx),
 (((-x^2)/y) dx, 2/x^4*y^4, ((-1)/(x^5*y)) dx),
 (0 dx, 2/x^5*y^4, (1/(x^6*y)) dx),
 ((x^5/y^2) dx, 2/x*y^3, ((-1)/(x^2*y^2)) dx),
 (((-x^4)/y^2) dx, 2/x^2*y^3, (1/(x^3*y^2)) dx),
 (0 dx, 2/x^3*y^3, 0 dx),
 ((x^2/y^2) dx, 2/x^4*y^3, ((-1)/(x^5*y^2)) dx),
 (0 dx, 2/x*y^2, ((-1)/(x^2*y^3)) dx),
 ((x^4/y^3) dx, 2/x^2*y^2, (1/(x^3*y^3)) dx),
 (((-x^5)/y^4) dx, 2/x*y, ((-1)/(x^2*y^4)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?7h[2/x*y^4,
 2/x^2*y^4,
 2/x^3*y^4,
 2/x^4*y^4,
 2/x^5*y^4,
 2/x*y^3,
 2/x^2*y^3,
 2/x^3*y^3,
 2/x^4*y^3,
 2/x*y^2,
 2/x^2*y^2,
 2/x*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.cohomology_of_structure_sheaf_basis()[0]).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(C.cohomology_of_structure_sheaf_basis()[0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7ld[0]).cordinates()[?7h[?12l[?25h[?25l[?7le[0]).cordinates()[?7h[?12l[?25h[?25l[?7l_[0]).cordinates()[?7h[?12l[?25h[?25l[?7lrh[0]).coordinates()[?7h[?12l[?25h[?25l[?7la[0]).cordinates()[?7h[?12l[?25h[?25l[?7lm[0]).cordinates()[?7h[?12l[?25h[?25l[?7l_[0]).cordinates()[?7h[?12l[?25h[?25l[?7lb[0]).cordinates()[?7h[?12l[?25h[?25l[?7la[0]).cordinates()[?7h[?12l[?25h[?25l[?7ls[0]).cordinates()[?7h[?12l[?25h[?25l[?7li[0]).cordinates()[?7h[?12l[?25h[?25l[?7ls[0]).cordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis[0]).coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 autom(C.de_rham_basis[Integer(0)]).coordinates()

TypeError: 'method' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis[0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0]).cordinates()[?7h[?12l[?25h[?25l[?7l)[0]).cordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[0]).coordinates()

[?7h[?12l[?25h[?2004lself ((1/y) dx, 0, (1/y) dx)
[?7h[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis()[0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates()[?7h[?12l[?25h[?25l[?7l1]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()

File <string>:71, in coordinates(self)

AttributeError: 'superelliptic_cech' object has no attribute 'coorinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, 0, (1/y) dx)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [21], in <cell line: 1>()
----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()

File <string>:71, in coordinates(self)

File <string>:56, in coordinates(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, 0, (1/y) dx)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()

File <string>:71, in coordinates(self)

TypeError: unsupported operand type(s) for +: 'sage.modules.vector_modn_dense.Vector_modn_dense' and 'list'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, 0, (1/y) dx)
[?7h(1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:74, in coordinates(self, basis)

TypeError: unsupported operand type(s) for /: 'superelliptic_form' and 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:75, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:79, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller().diffn().frobeniu()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y/(C.x^2+C.x)

[?7h[?12l[?25h[?2004l[?7h(1/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y/(C.x^2+C.x)).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler().f[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller().f

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().f[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller().t

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux_f_t_0 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), V((1/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:82, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().t[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x.teichmuller().t[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux_f_t_0 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V((1/(x^4 + 2*x^3 + 2*x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:82, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:84, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:84, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (0*C.x).pth_root()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)*C.dx[?7h[?12l[?25h[?25l[?7l.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC*y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l*y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2*y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^2*y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l/x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lx)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((-C.

....: x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lx^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7l....: 

....: [?7h[?12l[?25h[?25l[?7l(



)[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx

....: 

....: )

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx

....: 

....: )[?7h[?12l[?25h[?25l[?7l(



[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7la(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l=(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lsage: a = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7la = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.r() == -(C.x)^(-1)*C.y.diffn() + C.y*()^(-2)*dx[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U

 a.is_regular_on_U0    

 a.is_regular_on_Uinfty





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0

 a.is_regular_on_U0    



 <unknown> [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U0

[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic_form.is_regular_on_U0 of ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7l((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.is_regular_on_U0[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7la.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.de_rham_basis()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7lb = C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = 4*b[0][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC = C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l = C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lutom(C.de_rham_bais()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[0]).coordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b)

[?7h[?12l[?25h[?2004l[?7h(((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b).coordinates()

[?7h[?12l[?25h[?2004l[?7h(1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: autom(B) - B - A

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().t[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l(x^2+C.x)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (C.y/(C.x^2+C.x)).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lautomB) - B - A[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lDautom(B) - B - A[?7h[?12l[?25h[?25l[?7l autom(B) - B - A[?7h[?12l[?25h[?25l[?7l=autom(B) - B - A[?7h[?12l[?25h[?25l[?7l autom(B) - B - A[?7h[?12l[?25h[?25l[?7lsage: D = autom(B) - B - A

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD = autom(B) - B - A[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.r()

[?7h[?12l[?25h[?2004l[?7h(0 dx, (1/(x^2 + x))*y, ((-x^2 - x + 1)/(x^2*y + x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.r()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-D.r().f.difn()[?7h[?12l[?25h[?25l[?7lsage: D.r().omega8 == -D.r().f.diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.r().omega8 == -D.r().f.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.r().omega8 == -D.r().f.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x))[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= (C.y/(C.x^2+C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: D.f -= (C.y/(C.x^2+C.x)).teichmuller()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.f -= (C.y/(C.x^2+C.x)).teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.omega8 = D.omega0 - D.f.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lsage: D

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), V((1/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: D.omega0.h2 = 0*C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega0.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf -= (C.y/(C.x^2+C.x)).teichmuller()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2 + C.x + C.one).verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: D.f -= (C.y/(C.x^2 + C.x + C.one)).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.f -= (C.y/(C.x^2 + C.x + C.one)).verschiebung()[?7h[?12l[?25h[?25l[?7lomega0.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lf -= (C.y/(C.x^2+C.x)).techmuller()[?7h[?12l[?25h[?25l[?7lomega8 = D.omega0 - D.f.dffn()[?7h[?12l[?25h[?25l[?7lsage: D.omega8 = D.omega0 - D.f.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lsage: D

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V((1/(x^4 + 2*x^3 + 2*x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: D.omega8.h2 = 0*C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega8.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf -= (C.y/(C.x^2 + C.x + C.one)).verschiebung()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2/(x^4 + 2*x^3 + 2*x^2 + x))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7lC/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l./(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7lo/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7ln/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7le/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l/x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l.x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l.x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l.x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)*C.y[?7h[?12l[?25h[?25l[?7l.x)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((2*C.one/(C.x^4 + 2*C.x^3 + 2*C.x^2 + C.x))*C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.f += ((2*C.one/(C.x^4 + 2*C.x^3 + 2*C.x^2 + C.x))*C.y).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.f += ((2*C.one/(C.x^4 + 2*C.x^3 + 2*C.x^2 + C.x))*C.y).verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega8.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: D.omega0 - D.f.diffn() == D.omega8

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega0 - D.f.diffn() == D.omega8[?7h[?12l[?25h[?25l[?7lsage: D

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l/^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx*y + y) dx[?7h[?12l[?25h[?25l[?7l.x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + y) dx[?7h[?12l[?25h[?25l[?7l.y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy) dx[?7h[?12l[?25h[?25l[?7l.y) dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7la(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l=(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7lsage: aa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

[?7h[?12l[?25h[?2004l  Input In [30]
    aa = (-C.x**Integer(3) + C.x**Integer(2) + C.x)/(C.x**Integer(2)*C.y + C.x*C.y + C.y))* C.dx
                                                                                         ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: aa.is_regular_on_U

 aa.is_regular_on_U0    

 aa.is_regular_on_Uinfty





 [?7h[?12l[?25h[?25l[?7l0

 aa.is_regular_on_U0    



 <unknown> [?7h[?12l[?25h[?25l[?7linfty

 aa.is_regular_on_U0    

 aa.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aa.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7laa.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aa.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0 = B.omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B.omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0

[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B0.r()

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0.r()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l = B.omega0[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.*C.y.difn()[?7h[?12l[?25h[?25l[?7lt*C.y.difn()[?7h[?12l[?25h[?25l[?7le*C.y.difn()[?7h[?12l[?25h[?25l[?7li*C.y.difn()[?7h[?12l[?25h[?25l[?7lc*C.y.difn()[?7h[?12l[?25h[?25l[?7lh*C.y.difn()[?7h[?12l[?25h[?25l[?7lm*C.y.difn()[?7h[?12l[?25h[?25l[?7lu*C.y.difn()[?7h[?12l[?25h[?25l[?7lk*C.y.difn()[?7h[?12l[?25h[?25l[?7lk*C.y.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn()[?7h[?12l[?25h[?25l[?7ll*C.y.difn()[?7h[?12l[?25h[?25l[?7ll*C.y.difn()[?7h[?12l[?25h[?25l[?7le*C.y.difn()[?7h[?12l[?25h[?25l[?7lr*C.y.difn()[?7h[?12l[?25h[?25l[?7l(*C.y.difn()[?7h[?12l[?25h[?25l[?7l()*C.y.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7lt.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7li.difn()[?7h[?12l[?25h[?25l[?7lc.difn()[?7h[?12l[?25h[?25l[?7lh.difn()[?7h[?12l[?25h[?25l[?7lm.difn()[?7h[?12l[?25h[?25l[?7lu.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7lr.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lsage: B0 - C.x.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 - C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B0 -= C.x.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0

[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().t[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x*C.y.diffn() == B.r()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 C.x*C.y.diffn() == B.r()

File <string>:12, in __eq__(self, other)

AttributeError: 'superelliptic_cech' object has no attribute 'reduce'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.y.diffn() == B.r()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lor()[?7h[?12l[?25h[?25l[?7lomr()[?7h[?12l[?25h[?25l[?7ler()[?7h[?12l[?25h[?25l[?7lgr()[?7h[?12l[?25h[?25l[?7lar()[?7h[?12l[?25h[?25l[?7l0r()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x*C.y.diffn() == B.omega0.r()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:84, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= B.omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB.omega0[?7h[?12l[?25h[?25l[?7lsage: B0 = B.omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B.omega0[?7h[?12l[?25h[?25l[?7l = C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = B.omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: B0 -= C.x.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0

[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B8 = B.omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 = B.omega8[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B.r().omega8

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsB.r().omega8[?7h[?12l[?25h[?25l[?7leB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7loB.r().omega8[?7h[?12l[?25h[?25l[?7lnB.r().omega8[?7h[?12l[?25h[?25l[?7ldB.r().omega8[?7h[?12l[?25h[?25l[?7l(B.r().omega8[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l_B.r().omega8[?7h[?12l[?25h[?25l[?7lpB.r().omega8[?7h[?12l[?25h[?25l[?7laB.r().omega8[?7h[?12l[?25h[?25l[?7ltB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7lhB.r().omega8[?7h[?12l[?25h[?25l[?7ljB.r().omega8[?7h[?12l[?25h[?25l[?7l(B.r().omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(B.r().omega8)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(B.r().omega8)

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: u = C.one

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l8 = B.omega8[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B8 -= u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 -= u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B8

[?7h[?12l[?25h[?2004l[?7h[(1/(x^4 + 2*x^2))*y] d[x] + V(((x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8[?7h[?12l[?25h[?25l[?7l -= u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+= u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: B8 += u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B8 += u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B8

[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8[?7h[?12l[?25h[?25l[?7l.r().omega8[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l/y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly)* C.dx[?7h[?12l[?25h[?25l[?7l.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7lC)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7lo)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7ln)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7le)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx

[?7h[?12l[?25h[?2004l[?7h((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l=((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7lsage: a = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls_regular_on_U0()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7lf()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7ly()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l((2*x^6 + 2)/(x^8 + 2*x^6))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((2*x^6 + 2)/(x^8 + 2*x^6))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6)*C.y[?7h[?12l[?25h[?25l[?7l.x^6)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7lo)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7ln)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 + 2*C.one)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7lsage: b = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?7h[?12l[?25h[?25l[?7l.r().coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?7h[?12l[?25h[?25l[?7l.r().coordinates()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: b.expansion

 b.expansion         

 b.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 b.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 b.expansion         

 b.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lb.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?7h[?12l[?25h[?25l[?7la.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -= u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l8 = B.omega8[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= B.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = B.omega0[?7h[?12l[?25h[?25l[?7l-= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8 = B.omega8[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l().omega8[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lu = C.one[?7h[?12l[?25h[?25l[?7l/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.x)^2[?7h[?12l[?25h[?25l[?7lB8 -= u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7la = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lb = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.y.diffn() == B.omega0.r()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l()[1][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= B.omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0[?7h[?12l[?25h[?25l[?7lsage: B0 = B.omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B.omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B0 - C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((x^5 + x^3)/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 - C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7laB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: aaB8 - C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [75], in <cell line: 1>()
----> 1 aaB8 - C.y.teichmuller().diffn()

NameError: name 'aaB8' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7laaB8 - C.yteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lv.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B8 + C.v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [77], in <cell line: 1>()
----> 1 B8 + C.v.teichmuller().diffn()

AttributeError: 'superelliptic' object has no attribute 'v'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 + C.v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lv.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B8 + v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((x^8 + x^6 - x^5 + x^4 + x^3 + x^2 + x - 1)/(x^9*y - x^8*y)) dx) + dV([((2*x^6 + x^3 + 1)/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 + v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l- v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: B8 - v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(2/(x^3 + 2*x))*y] d[x] + V(((-x^8 - x^6 - x^5 - x^4 + x^3 - x^2 + x + 1)/(x^9*y + x^8*y)) dx) + dV([((2*x^6 + 2*x^3 + 1)/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l().omega8[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsB.r().omega8[?7h[?12l[?25h[?25l[?7leB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7loB.r().omega8[?7h[?12l[?25h[?25l[?7lnB.r().omega8[?7h[?12l[?25h[?25l[?7ldB.r().omega8[?7h[?12l[?25h[?25l[?7l_B.r().omega8[?7h[?12l[?25h[?25l[?7lpB.r().omega8[?7h[?12l[?25h[?25l[?7laB.r().omega8[?7h[?12l[?25h[?25l[?7ltB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7lhB.r().omega8[?7h[?12l[?25h[?25l[?7l(B.r().omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(B.r().omega8)

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lCv.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lvteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsecod_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lCv.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lvteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lC.geus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: lo

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [83], in <cell line: 1>()
----> 1 lo

NameError: name 'lo' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:26, in <module>

File <string>:84, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
[?7h[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
 ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lC.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: a.omega8

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: v^2 - u - u^3

[?7h[?12l[?25h[?2004l[?7h1/x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv^2 - u - u^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l u^3[?7h[?12l[?25h[?25l[?7l+ u^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v^2 - u + u^3

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv^2 - u + u^3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lu =C.one/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.x)^2[?7h[?12l[?25h[?25l[?7la.omega8[?7h[?12l[?25h[?25l[?7lsage: a.omega8

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l*([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a.omega8 + v.diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 a.omega8 + v.diffn()

File <string>:81, in __add__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'h1'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 + v.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltdifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lidifn()[?7h[?12l[?25h[?25l[?7lcdifn()[?7h[?12l[?25h[?25l[?7lhdifn()[?7h[?12l[?25h[?25l[?7lmdifn()[?7h[?12l[?25h[?25l[?7ludifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lrdifn()[?7h[?12l[?25h[?25l[?7l(difn()[?7h[?12l[?25h[?25l[?7l()difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l/difn()[?7h[?12l[?25h[?25l[?7ldifn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a.omega8 + v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(2/(x^3 + 2*x))*y] d[x] + V(((x^2 + 1)/(x^5*y)) dx) + dV([((x^2 + 1)/(x^5 + 2*x^3))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 + v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l- v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: a.omega8 - v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((-x^2 - 1)/(x^5*y)) dx) + dV([1/x^3*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lr() ==(Cx)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.r()

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv^2 - u + u^3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: v.diffn()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.diffn()[?7h[?12l[?25h[?25l[?7lar()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: a.omega8 - v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((-x^2 - 1)/(x^5*y)) dx) + dV([1/x^3*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lla[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7lf()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7ly()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 (a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()

AttributeError: 'superelliptic_function' object has no attribute 'is_regular_on_Uinfty'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a.omega8 - v.teichmuller().diffn()).h2.expansion()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 (a.omega8 - v.teichmuller().diffn()).h2.expansion()

TypeError: superelliptic_function.expansion() missing 1 required positional argument: 'pt'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).h2.expansion()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a.omega8 - v.teichmuller().diffn()).h2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^3 + 2*t^7 + 2*t^11 + t^15 + 2*t^19 + O(t^23)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lomega.is_regularon_Uinfty()[?7h[?12l[?25h[?25l[?7lh2.is_regular_onUinfty()[?7h[?12l[?25h[?25l[?7lexpansion()[?7h[?12l[?25h[?25l[?7l_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lresult.factor()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: regula

 regular_form

 regulator   





 [?7h[?12l[?25h[?25l[?7lr_form

 regular_form



 <unknown> [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: regular_form(C.dx)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lregular_form(C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form(C.dx)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm_witt_lift[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(C.de_rham_basis()[0])

[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rhm_basis()[1][?7h[?12l[?25h[?25l[?7lx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_regular_form at 0x7f293c63c4f0>) failed: NameError: name 'A' is not defined>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

[?7h[?12l[?25h[?2004l[?7h1 dx + 0 dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Input In [11] in <cell line: 1>
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:18 in <module>

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:8
    if self.dx.form = _sage_const_0 :
       ^
SyntaxError: cannot assign to attribute here. Maybe you meant '==' instead of '='?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lift.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_regular_form at 0x7f293c5f6ec0>) failed: AttributeError: 'superelliptic_function' object has no attribute 'form'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l(C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l()C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l.)C.dx).regular_form()[?7h[?12l[?25h[?25l[?7ly)C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l(C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l-C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l1C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l()C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l()*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*C.dx).regular_form()

[?7h[?12l[?25h[?2004l[?7h1 dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l ((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l=((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l ((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = ((C.y)^(-1)*C.dx).regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = ((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h1 dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lsage: A.form

[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic_regular_form.form of 1 dy>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.form[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.form()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lstalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()

File <string>:39, in crystalline_cohomology_basis(self, prec)

File <string>:15, in de_rham_witt_lift(cech_class, prec)

AttributeError: 'tuple' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()

File <string>:39, in crystalline_cohomology_basis(self, prec)

File <string>:15, in de_rham_witt_lift(cech_class, prec)

AttributeError: 'tuple' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form(C.dx)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_form(C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form(C.dx)

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lregular_form(C.dx)[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
 ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 B[Integer(0)].omega0.regular_form()

AttributeError: 'superelliptic_drw_form' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF = GF(4, 'a')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l0 - C.y.teichmler().diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsage: B01 = super

 super                          superelliptic_cech             superelliptic_drw_form         superelliptic_regular_drw_form supersingular_D               

 superelliptic                  superelliptic_drw/             superelliptic_form             superelliptic_regular_form     supersingular_j               

 superelliptic/                 superelliptic_drw_cech         superelliptic_function         superelliptic_witt                                           



 [?7h[?12l[?25h[?25l[?7lsupere





[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l

 B01.curve     B01.h2       

 B01.frobenius B01.omega    

 B01.h1        B01.r        

 

 [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l(relliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lre.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lu.sage')[?7h[?12l[?25h[?25l[?7ll.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lf.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7lm.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l[0].omega0.rular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohmology_basis()[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomlgy_basis()[?7h[?12l[?25h[?25l[?7lB = C.crystalline_chmology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7l





 



























 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 































 [?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l01= B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l

 B01.curve        B01.h2           B01.regular_form

 B01.frobenius    B01.omega                        

 B01.h1           B01.r                            [?7h[?12l[?25h[?25l[?7lcurve

 B01.curve       





 <unknown> [?7h[?12l[?25h[?25l[?7lh2

 B01.curve        B01.h2          [?7h[?12l[?25h[?25l[?7lregular_form

 B01.h2           B01.regular_form[?7h[?12l[?25h[?25l[?7l







[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 B01.regular_form()

File <string>:37, in regular_drw_form(omega)

TypeError: 'superelliptic' object is not callable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 













 [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 











 [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 









 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l01= B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7legular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 B01.regular_form()

File <string>:41, in regular_drw_form(omega)

TypeError: superelliptic_drw_form.__init__() takes 4 positional arguments but 5 were given
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 B01.regular_form()

AttributeError: 'superelliptic_drw_form' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l01.regular_form()[?7h[?12l[?25h[?25l[?7l1.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega8[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lnd_patch[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B01 = second_patch(B01)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = second_patch(B01)[?7h[?12l[?25h[?25l[?7lB[0].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 B01.regular_form()

AttributeError: 'NoneType' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: B01

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ qsage -i parsivelib galois Representations
make build/make/Makefile --stop
make[1]: Entering directory '/ext/sage/9.7'
make[1]: 'build/make/Makefile' is up to date.
make[1]: Leaving directory '/ext/sage/9.7'
build/bin/sage-logger \
	"cd build/make && ./install 'all-toolchain'" logs/install.log
tee: logs/install.log: Read-only file system
make[1]: Entering directory '/ext/sage/9.7/build/make'
make[1]: Leaving directory '/ext/sage/9.7/build/make'
*** ALL ENVIRONMENT VARIABLES BEFORE BUILD: ***
ANACONDA2019=/ext/anaconda-2019.03
ANACONDA2020=/ext/anaconda2020.02
ANACONDA2021=/ext/anaconda2021.11
ANACONDA2022=/ext/anaconda2022.05
ANACONDA3=/ext/anaconda3
ANACONDA5=/ext/anaconda5
BROWSER_PORT=6001
COCALC_CODE_PORT=6004
COCALC_EXTRA_ENV=e30=
COCALC_JUPYTERLAB_PORT=6002
COCALC_JUPYTER_PORT=6003
COCALC_NODE=kucalc-prod3-node-pbpa
COCALC_PLUTO_PORT=6005
COCALC_PROJECT_CONFIG=eyJxdW90YSI6eyJuZXR3b3JrIjp0cnVlLCJtZW1iZXJfaG9zdCI6dHJ1ZSwicHJpdmlsZWdlZCI6ZmFsc2UsIm1lbW9yeV9yZXF1ZXN0IjozMDAsImNwdV9yZXF1ZXN0IjowLjA1LCJkaXNrX3F1b3RhIjo4MDAwLCJtZW1vcnlfbGltaXQiOjEyMDAwLCJjcHVfbGltaXQiOjIsImlkbGVfdGltZW91dCI6MTgwMCwiYWx3YXlzX3J1bm5pbmciOmZhbHNlLCJkZWRpY2F0ZWRfdm0iOmZhbHNlLCJkZWRpY2F0ZWRfZGlza3MiOltdfX0=
COCALC_PROJECT_DATASTORE=false
COCALC_PROJECT_ID=6b7177d7-4a24-4810-937c-d1fa861bd29e
COCALC_PROJECT_IMAGE_NAME=ubuntu2004
COCALC_SECRET_TOKEN=/secrets/secret-token/token
COCALC_SSH_PORT=2222
COCALC_TERMINAL_FILENAME=.run.term-0.term
COCALC_ULIMIT_OPEN_FILES=10000
COCALC_USERNAME=user
DEBUG=project:*,cocalc:*
DEBUG_HIDE_DATE=yes
ELAN_HOME=/ext/lean
EXT=/ext
HISTCONTROL=ignoredups
HOME=/home/user
HOSTNAME=project-6b7177d7-4a24-4810-937c-d1fa861bd29e
HUB_PORT=6000
ISOCHRONES=/ext/data/isochrones
JULIA_DEPOT_PATH=/home/user/.julia:/ext/julia/depot/
JUPYTER_PATH=/ext/jupyter
LANG=en_US.UTF-8
LANGUAGE=en_US:en
LC_ALL=C.UTF-8
LESSCLOSE=/usr/bin/lesspipe %s %s
LESSOPEN=| /usr/bin/lesspipe %s
LESS_TERMCAP_se=
LESS_TERMCAP_so=
LS_COLORS=rs=0:di=01;34:ln=01;36:mh=00:pi=40;33:so=01;35:do=01;35:bd=40;33;01:cd=40;33;01:or=40;31;01:mi=00:su=37;41:sg=30;43:ca=30;41:tw=30;42:ow=34;42:st=37;44:ex=01;32:*.tar=01;31:*.tgz=01;31:*.arc=01;31:*.arj=01;31:*.taz=01;31:*.lha=01;31:*.lz4=01;31:*.lzh=01;31:*.lzma=01;31:*.tlz=01;31:*.txz=01;31:*.tzo=01;31:*.t7z=01;31:*.zip=01;31:*.z=01;31:*.dz=01;31:*.gz=01;31:*.lrz=01;31:*.lz=01;31:*.lzo=01;31:*.xz=01;31:*.zst=01;31:*.tzst=01;31:*.bz2=01;31:*.bz=01;31:*.tbz=01;31:*.tbz2=01;31:*.tz=01;31:*.deb=01;31:*.rpm=01;31:*.jar=01;31:*.war=01;31:*.ear=01;31:*.sar=01;31:*.rar=01;31:*.alz=01;31:*.ace=01;31:*.zoo=01;31:*.cpio=01;31:*.7z=01;31:*.rz=01;31:*.cab=01;31:*.wim=01;31:*.swm=01;31:*.dwm=01;31:*.esd=01;31:*.jpg=01;35:*.jpeg=01;35:*.mjpg=01;35:*.mjpeg=01;35:*.gif=01;35:*.bmp=01;35:*.pbm=01;35:*.pgm=01;35:*.ppm=01;35:*.tga=01;35:*.xbm=01;35:*.xpm=01;35:*.tif=01;35:*.tiff=01;35:*.png=01;35:*.svg=01;35:*.svgz=01;35:*.mng=01;35:*.pcx=01;35:*.mov=01;35:*.mpg=01;35:*.mpeg=01;35:*.m2v=01;35:*.mkv=01;35:*.webm=01;35:*.ogm=01;35:*.mp4=01;35:*.m4v=01;35:*.mp4v=01;35:*.vob=01;35:*.qt=01;35:*.nuv=01;35:*.wmv=01;35:*.asf=01;35:*.rm=01;35:*.rmvb=01;35:*.flc=01;35:*.avi=01;35:*.fli=01;35:*.flv=01;35:*.gl=01;35:*.dl=01;35:*.xcf=01;35:*.xwd=01;35:*.yuv=01;35:*.cgm=01;35:*.emf=01;35:*.ogv=01;35:*.ogx=01;35:*.aac=00;36:*.au=00;36:*.flac=00;36:*.m4a=00;36:*.mid=00;36:*.midi=00;36:*.mka=00;36:*.mp3=00;36:*.mpc=00;36:*.ogg=00;36:*.ra=00;36:*.wav=00;36:*.oga=00;36:*.opus=00;36:*.spx=00;36:*.xspf=00;36:
MAKE=make
MAKEFLAGS= V=1
MAKELEVEL=1
MAKE_TERMERR=/dev/pts/0
MAKE_TERMOUT=/dev/pts/0
MFLAGS=
MKL_THREADING_LAYER=GNU
MPLBACKEND=Agg
NLTK_DATA=/ext/data/nltk_data
NVM_INC=/cocalc/nvm/versions/node/v16.19.1/include/node
OLDPWD=/ext/sage/9.7
PATH=/ext/sage/9.7/build/bin:/ext/sage/9.7/src/bin:/ext/sage/9.7/local/bin:/cocalc/bin:/cocalc/src/smc-project/bin:/home/user/bin:/home/user/.local/bin:/ext/bin:/usr/lib/xpra:/opt/ghc/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/ext/data/homer/bin:/ext/data/weblogo:/usr/lib/postgresql/10/bin
PGHOST=localhost
PROMPT_COMMAND=history -a
PWD=/ext/sage/9.7/build/make
PYTHONPATH=/ext/sage/9.7/local
PYTHONUSERBASE=/home/user/.local
QT_QPA_PLATFORM=xcb
SAGE_ATLAS_LIB=/usr/lib/
SAGE_ENV_CONFIG_SOURCED=1
SAGE_LOCAL=/ext/sage/9.7/local
SAGE_LOGFILE=logs/install.log
SAGE_LOGS=/ext/sage/9.7/logs/pkgs
SAGE_NUM_THREADS=1
SAGE_NUM_THREADS_PARALLEL=4
SAGE_ORIG_PATH=/cocalc/bin:/cocalc/src/smc-project/bin:/home/user/bin:/home/user/.local/bin:/ext/bin:/usr/lib/xpra:/opt/ghc/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/ext/data/homer/bin:/ext/data/weblogo:/usr/lib/postgresql/10/bin
SAGE_ORIG_PATH_SET=True
SAGE_PKGCONFIG=/ext/sage/9.7/local/lib/pkgconfig
SAGE_ROOT=/ext/sage/9.7
SAGE_SHARE=/ext/sage/9.7/local/share
SAGE_SRC=/ext/sage/9.7/src
SAGE_VENV=/ext/sage/9.7/local/var/lib/sage/venv-python3.10.5
SCREENDIR=/tmp/screen
SHELL=/bin/bash
SHLVL=3
SMC=/tmp/.cocalc
TERM=xterm-256color
TZ=Etc/UTC
USER=user
XDG_RUNTIME_DIR=/tmp/xdg-runtime-user
_=/usr/bin/env
_JAVA_OPTIONS=-Xms64m
***********************************************
make[1]: Entering directory '/ext/sage/9.7/build/make'
make --no-print-directory toolchain
make[2]: Nothing to be done for 'toolchain'.
make --no-print-directory toolchain-deps
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make[1]: Leaving directory '/ext/sage/9.7/build/make'

real	0m0.278s
user	0m0.238s
sys	0m0.020s
Sage build/upgrade complete!

Error: package 'parsivelib' not found
Note: if it is an old-style package, installing these is no longer supported
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[0].omega0.regular_frm()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0][?7h[?12l[?25h[?25l[?7l0B[0][?7h[?12l[?25h[?25l[?7l B[0][?7h[?12l[?25h[?25l[?7l=B[0][?7h[?12l[?25h[?25l[?7l B[0][?7h[?12l[?25h[?25l[?7lsage: B0 = B[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.omega8 - compare[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomrphic_differentials_basis()[-1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = B[0].omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = B[0].omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage -i parsivelib galois Representations[?7h[?12l[?25h[?25l[?7lecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lnd_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: second_patch(om)

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(2*x/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(om).r()

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion(pt = (-1, 0))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsom.r()[?7h[?12l[?25h[?25l[?7leom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7lnom.r()[?7h[?12l[?25h[?25l[?7ldom.r()[?7h[?12l[?25h[?25l[?7l_om.r()[?7h[?12l[?25h[?25l[?7lpom.r()[?7h[?12l[?25h[?25l[?7laom.r()[?7h[?12l[?25h[?25l[?7ltom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lhom.r()[?7h[?12l[?25h[?25l[?7l(om.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(om.r())

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsom[?7h[?12l[?25h[?25l[?7leom[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0].omega8[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = second_patch(om)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = second_patch(om)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion(p = (-1, 0))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lgular_form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(x*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7l().r([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l = B[0].omega8[?7h[?12l[?25h[?25l[?7lB0[][?7h[?12l[?25h[?25l[?7lom[].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].omega8[?7h[?12l[?25h[?25l[?7l1].omega8[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = B[1].omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = B[1].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l = B[1].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lom = second_patch(om)[?7h[?12l[?25h[?25l[?7lsage: om = second_patch(om)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = second_patch(om)[?7h[?12l[?25h[?25l[?7lB[1].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [2*x] d[y] + V(((-x^10 - x^8 - x^6 + x^2)/(x^2*y - y)) dx) + dV((2*x^4 + 2*x^2 + 2)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(R)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: Rx

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-x^10 - x^8 - x^6 + x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^10 - x^8 - x^6 + x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^10 - x^8 - x^6 + x^2).quo_rem(x^2 - 1)

[?7h[?12l[?25h[?2004l[?7h(2*x^8 + x^6 + 1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = de_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0omega.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x] d[y] + V(0 dx) + dV((2*x^4 + 2*x^2 + 2)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l8.regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lseta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7leta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lceta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7loeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lneta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7ldeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7l_eta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lpeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7laeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lteta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lceta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lheta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7l(eta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(eta2.omega8).regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [2*x] d[y] + V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV((2*x^4 + 2*x^2 + 2)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)

[?7h[?12l[?25h[?2004l[?7h(2*x^8 + x^6 + 2, x^8 + 2*x^4 + 2*x^2 + 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lstalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lEC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lTC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lAC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l2C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: ETA2 - eta2

[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx) + dV([(x^4 + x^2 + 1)*y]), V((x^4 + x^2 + 1)*y), V(((x^8 - x^6 + 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8 - x^6 + 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^8 - x^6 + 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^8 - x^6 + 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 + 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^6 + 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/y) dx[?7h[?12l[?25h[?25l[?7lC)/y) dx[?7h[?12l[?25h[?25l[?7l.)/y) dx[?7h[?12l[?25h[?25l[?7lo)/y) dx[?7h[?12l[?25h[?25l[?7ln)/y) dx[?7h[?12l[?25h[?25l[?7le)/y) dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy) dx[?7h[?12l[?25h[?25l[?7l.y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x^8 - C.x^6 + C.one)/C.y)*C.dx

[?7h[?12l[?25h[?2004l  Input In [11]
    (C.x**Integer(8) - C.x**Integer(6) + C.one)/C.y)*C.dx
                                                   ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^8 - C.x^6 + C.one)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7lsage: (C.x^8 - C.x^6 + C.one)/C.y*C.dx

[?7h[?12l[?25h[?2004l[?7h((x^8 - x^6 + 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^8 - C.x^6 + C.one)/C.y*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^6 + C.one)/C.y*C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x^8 - C.x^6 + C.one)/C.y*C.dx).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-16 + t^-8 + O(t^-6)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loeta[?7h[?12l[?25h[?25l[?7lmeta[?7h[?12l[?25h[?25l[?7l eta[?7h[?12l[?25h[?25l[?7l eta[?7h[?12l[?25h[?25l[?7leta[?7h[?12l[?25h[?25l[?7l=eta[?7h[?12l[?25h[?25l[?7l eta[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = eta.omega8

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 om = eta.omega8

AttributeError: 'function' object has no attribute 'omega8'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = eta.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = eta2.omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = eta2.omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsom.r()[?7h[?12l[?25h[?25l[?7leom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7lnom.r()[?7h[?12l[?25h[?25l[?7ldom.r()[?7h[?12l[?25h[?25l[?7l_om.r()[?7h[?12l[?25h[?25l[?7lpom.r()[?7h[?12l[?25h[?25l[?7laom.r()[?7h[?12l[?25h[?25l[?7ltom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lhom.r()[?7h[?12l[?25h[?25l[?7l(om.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(om.r())

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.diffn()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = eta2.omega8[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om - u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^4 + 2*x^2))*y] d[x] + V(((-x^18 - x^16 - x^14 - x^10 - x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om + u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.frobnius()[?7h[?12l[?25h[?25l[?7l = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lmom + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l1om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = om + u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.frbenis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: om1.omega.expansion

 om1.omega.expansion         

 om1.omega.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 om1.omega.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 om1.omega.expansion         

 om1.omega.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.omega.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-16 + 2*t^-8 + O(t^-6)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lom1.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.frobenius()

[?7h[?12l[?25h[?2004l[?7h((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lom1.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + t^8 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: om1.h2.expansion

 om1.h2.expansion         

 om1.h2.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 om1.h2.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 om1.h2.expansion         

 om1.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.h2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lresult.omega8 == compare False
result.omega8 == compare False
[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lresult.omega8 == compare False
result.omega8 - compare dV([((x^2 + 1)/x^3)*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

































 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lEC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lTC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lAC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l2C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lresult.omega8 == compare False
result.omega8 - compare dV([((x^2 + 1)/x^3)*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 























 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





















 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lresult.omega8 == compare False
result.omega8 - compare dV([((2*x^2 + 1)/x^3)*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 











 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 









 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lresult.omega8 == compare False
result.omega8 - compare dV([1/x^3*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lresult.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loETA2[?7h[?12l[?25h[?25l[?7lmETA2[?7h[?12l[?25h[?25l[?7l ETA2[?7h[?12l[?25h[?25l[?7l=ETA2[?7h[?12l[?25h[?25l[?7l ETA2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = ETA2.omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lpatch(om.r())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: second_patch(om)

[?7h[?12l[?25h[?2004l[?7h[(2/(x^2 + 2))*y] d[x] + V(((-x^2)/y) dx) + dV([(1/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lETA2= C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lom =ETA2.omeg8[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lETA2= C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom1.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobeniu().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lETA2= C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom1.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobeniu().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7l = eta2.omega8[?7h[?12l[?25h[?25l[?7l.omega8[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^6 + C.one)/C.y*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.x^8 - C.x^6 + C.one)/C.y*C.dx[?7h[?12l[?25h[?25l[?7l)*C.dx[?7h[?12l[?25h[?25l[?7lETA2 -eta2[?7h[?12l[?25h[?25l[?7l=C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)[?7h[?12l[?25h[?25l[?7lsecond_patch(eta2.omega8).regular_form()[?7h[?12l[?25h[?25l[?7leta2.omega0.rgular_form()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llod('init.sage')[?7h[?12l[?25h[?25l[?7l(-x^10 - x^8 - x^6 + x^2).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7l(-x^10 - x^8 - x^6 + x^2).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7let2[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lsecond_patch(ta2.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l(C.x^8- C.x^6 + C.one)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7l(C.x^8 - C.x^6 + C.one)/C.y*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lom = eta.omega8[?7h[?12l[?25h[?25l[?7l2.omega8[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.x)^2[?7h[?12l[?25h[?25l[?7lom - u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1 = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lh2.expanion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lom =ETA2.omeg8[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: om - u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^4 + 2*x^2))*y] d[x] + V(((x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om + u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAom + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = om + u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.for()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: A.omega.expansion

 A.omega.expansion         

 A.omega.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 A.omega.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 A.omega.expansion         

 A.omega.expansion_at_infty[?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.omega.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^4 + t^8 + 2*t^12 + O(t^14)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lA.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion

 A.h2.expansion         

 A.h2.expansion_at_infty

 



 [?7h[?12l[?25h[?25l[?7l

 A.h2.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 A.h2.expansion         

 A.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.h2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lutom(B) - B - A[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7leta2lift)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(ETA2).coordinates()

[?7h[?12l[?25h[?2004l(1, 1)
result.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 autom(ETA2).coordinates()

File <string>:84, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l1 = C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ETA1 = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lresult.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laETA2 - ETA1[?7h[?12l[?25h[?25l[?7luETA2 - ETA1[?7h[?12l[?25h[?25l[?7ltETA2 - ETA1[?7h[?12l[?25h[?25l[?7loETA2 - ETA1[?7h[?12l[?25h[?25l[?7lmETA2 - ETA1[?7h[?12l[?25h[?25l[?7l(ETA2 - ETA1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() - ETA1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7luautom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7lxautom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l=autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = autom(ETA2) - ETA1 - ETA2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux1 = aux

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1 = aux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7lsage: C.y/(C.x^2+C.x)

[?7h[?12l[?25h[?2004l[?7h(1/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y/(C.x^2+C.x).expansion_at_infty()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 C.y/(C.x**Integer(2)+C.x).expansion_at_infty()

File <string>:75, in __truediv__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y/(C.x^2+C.x)).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7laux1 = aux[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lautom(ETA2).coordates()[?7h[?12l[?25h[?25l[?7lA.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7lomega.expansionat_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lh2.expansion_atinfty()[?7h[?12l[?25h[?25l[?7lautom(ETA2).coordinates[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalle_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7laux = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = aux[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7laux1 = aux[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = aux[?7h[?12l[?25h[?25l[?7l = aux[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux1

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux1.f.t = 0*C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.f.t = 0*C.x[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux1.omega0.h2 = 0*Cx

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 aux1.omega0.h2 = Integer(0)*Cx

NameError: name 'Cx' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.omega0.h2 = 0*Cx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux1.omega0.h2 = 0*C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.omega0.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = 0*C.x[?7h[?12l[?25h[?25l[?7l = 0*C.x[?7h[?12l[?25h[?25l[?7lf = 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-= 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7lf -= aux.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux1.f -= aux.omega0.h2.verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.f -= aux.omega0.h2.verschiebung()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux1

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0.h2.verschiebung()[?7h[?12l[?25h[?25l[?7lomega0.h2 = 0*Cx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux1.omega8 = aux1.omega0 - aux1.f.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.omega8 = aux1.omega0 - aux1.f.diffn()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux1

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((2*x^5 + 2*x^4 + x^3 + 2*x^2 + x + 2)/(x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega8 = aux1.omega0 - aux1.f.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(aux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)aux1[?7h[?12l[?25h[?25l[?7l.)aux1[?7h[?12l[?25h[?25l[?7lx)aux1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^aux1[?7h[?12l[?25h[?25l[?7l(aux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l()paux1[?7h[?12l[?25h[?25l[?7l-aux1[?7h[?12l[?25h[?25l[?7l1aux1[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l(aux1[?7h[?12l[?25h[?25l[?7l-aux1[?7h[?12l[?25h[?25l[?7lpaux1[?7h[?12l[?25h[?25l[?7l+aux1[?7h[?12l[?25h[?25l[?7l1aux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l()*aux1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7le(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7ls(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7lt(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l (C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l=(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l (C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: test = (C.x)^(-p+1)*aux1.omega0.omega

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltest = (C.x)^(-p+1)*aux1.omega0.omega[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: test

[?7h[?12l[?25h[?2004l[?7h((-x^2 + x + 1)/(x^3*y + x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lftest[?7h[?12l[?25h[?25l[?7lctest[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7l=test[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7lstest[?7h[?12l[?25h[?25l[?7lutest[?7h[?12l[?25h[?25l[?7lptest[?7h[?12l[?25h[?25l[?7letest[?7h[?12l[?25h[?25l[?7lrtest[?7h[?12l[?25h[?25l[?7letest[?7h[?12l[?25h[?25l[?7lltest[?7h[?12l[?25h[?25l[?7lltest[?7h[?12l[?25h[?25l[?7lltest[?7h[?12l[?25h[?25l[?7litest[?7h[?12l[?25h[?25l[?7lptest[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7litest[?7h[?12l[?25h[?25l[?7lctest[?7h[?12l[?25h[?25l[?7l_test[?7h[?12l[?25h[?25l[?7lftest[?7h[?12l[?25h[?25l[?7lutest[?7h[?12l[?25h[?25l[?7lntest[?7h[?12l[?25h[?25l[?7lctest[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7litest[?7h[?12l[?25h[?25l[?7lotest[?7h[?12l[?25h[?25l[?7lntest[?7h[?12l[?25h[?25l[?7l(test[?7h[?12l[?25h[?25l[?7lCtest[?7h[?12l[?25h[?25l[?7l,test[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fct = superellliptic_function(C, test.form)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [65], in <cell line: 1>()
----> 1 fct = superellliptic_function(C, test.form)

NameError: name 'superellliptic_function' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = superellliptic_function(C, test.form)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liptic_function(C, test.form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fct = superelliptic_function(C, test.form)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = superelliptic_function(C, test.form)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fct.pth_root()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [67], in <cell line: 1>()
----> 1 fct.pth_root()

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.y.diffn( == B.omega0.r()[?7h[?12l[?25h[?25l[?7l.teichmuller().t[?7h[?12l[?25h[?25l[?7lteichmuller().t[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (3*C.x.teichmuller()).diffn()

[?7h[?12l[?25h[?2004l[?7hdV([x^3])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn()

[?7h[?12l[?25h[?2004l[?7h[2] d[x]dV([x^3])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: ETA1

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn()

[?7h[?12l[?25h[?2004l[?7h[2] d[x]dV([x^3])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn()

[?7h[?12l[?25h[?2004l[?7h[2] d[x] + dV([x^3])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2(C.x.teichmuler()).difn()[?7h[?12l[?25h[?25l[?7l*(C.x.teichmuler()).difn()[?7h[?12l[?25h[?25l[?7l((C.x.teichmuler()).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: 2*((C.x.teichmuller()).diffn())

[?7h[?12l[?25h[?2004l[?7h[2] d[x] + V((x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn() == 2*((C.x.teichmuller()).diffn())

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn() == 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load('init.sage')

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[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + dV([x^3]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()

[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + dV([x^3]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller())diffn())[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().diffn(), 2*((C.xteichmuller()).diffn())[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn(), 2*((C.x.teichmuller()).diffn())

[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn(), 2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()C.x.teichmuler().difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()).difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (2*(C.x.teichmuller())).diffn(), 2*((C.x.teichmuller()).diffn())

[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*b[0][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn())

[?7h[?12l[?25h[?2004l[?7h + V((x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004lTrue False
[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004l(self.omega - other.omega).cartier() - H.diffn() (-1) dx
[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004lH 2*x
(self.omega - other.omega).cartier() - H.diffn() (-1) dx
[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004lH 2*x
(self.omega - other.omega).cartier() 1 dx
[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct.pth_root()[?7h[?12l[?25h[?25l[?7lor i in range(10):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lac[0].coordinates():[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for a in range(0, 9):

....: [?7h[?12l[?25h[?25l[?7lp = 3[?7h[?12l[?25h[?25l[?7lrint(type(a))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*(C.x.teichmuler().difn() = 3*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7la*(C.x.teichmuler().difn() = 3*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn()))[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn()))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7laC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(a*(C.x.teichmuller().diffn()) == a*(C.x.teichmuller()).diffn())

....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(0, 9):

....:     print(a*(C.x.teichmuller().diffn()) == a*(C.x.teichmuller()).diffn())

....: 

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
True
True
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.teichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lresult.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: ETA1 = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lresult.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7lsage: ETA2

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2[?7h[?12l[?25h[?25l[?7l1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.regular_form()[?7h[?12l[?25h[?25l[?7le_ham_basis()[1][?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*(C.x.teichmuller())).diffn(), 2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (3/2)%9

[?7h[?12l[?25h[?2004l[?7h6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lteichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3/2)%9[?7h[?12l[?25h[?25l[?7l-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)[?7h[?12l[?25h[?25l[?7l1/2)*C..teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%9[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (-1/2)%9

[?7h[?12l[?25h[?2004l[?7h4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 3*C.x.teichmuller()

[?7h[?12l[?25h[?2004l[?7hV(x^3)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 3*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV((x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^7 + x^3 + x)/(x^2*y - y))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^7 + x^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l/x^7 + x^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^7 + x^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l.x^7 + x^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l.x^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^2*y - y)[?7h[?12l[?25h[?25l[?7l.x^2*y - y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy - y)[?7h[?12l[?25h[?25l[?7l.y - y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy)[?7h[?12l[?25h[?25l[?7l.y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l()C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l()*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l.)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7ly)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l(*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l()*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l3)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()+[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2*C.dx+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 ((-C.x**Integer(7) + C.x**Integer(3) + C.x)/(C.x**Integer(2)*C.y - C.y)) == (C.y)**(-Integer(3))*C.x**Integer(2)*C.dx+ Integer(2)*C.x**Integer(8)*(C.y)**(-Integer(3))+(C.x**Integer(5) - C.x**Integer(7))/(Integer(2)*C.y**Integer(5))

File <string>:19, in __add__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2*C.dx+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l*C.dx+ 2*C.x^8*(C.y^-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l3*Cx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.ydiffn()[?7h[?12l[?25h[?25l[?7l((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2*C.dx+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3+C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7lmC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = C.de_rham_basis()[1].omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsom[?7h[?12l[?25h[?25l[?7leom[?7h[?12l[?25h[?25l[?7lcom[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lnom[?7h[?12l[?25h[?25l[?7ldom[?7h[?12l[?25h[?25l[?7l_om[?7h[?12l[?25h[?25l[?7lpom[?7h[?12l[?25h[?25l[?7laom[?7h[?12l[?25h[?25l[?7ltom[?7h[?12l[?25h[?25l[?7lcom[?7h[?12l[?25h[?25l[?7lhom[?7h[?12l[?25h[?25l[?7l(om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(om)

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7l().r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(om).regular_form()

[?7h[?12l[?25h[?2004l[?7h2*x dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()[Integer(1)]

File <string>:52, in crystalline_cohomology_basis(self, prec)

File <string>:23, in de_rham_witt_lift(cech_class, prec)

NameError: name 'omega' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()[Integer(1)]

File <string>:52, in crystalline_cohomology_basis(self, prec)

File <string>:24, in de_rham_witt_lift(cech_class, prec)

File <string>:13, in de_rham_witt_lift_form8(omega)

NameError: name 'g' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.y.diffn() == B.mega0.r()[?7h[?12l[?25h[?25l[?7l.teichmuller().t[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lhm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAC.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: A = C.x.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B[0][?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0C.x/C.y*C.dx[?7h[?12l[?25h[?25l[?7l(C.x/C.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B = de_rham_witt_lift_form0(C.x/C.y*C.dx)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A == B

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1 = de_rham_wittliftC.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de_rham_basis()[0])





























 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
sage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())


[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



























 [?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l10[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: ETA1 = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 









 [?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1 - ETA1

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3)/y) dx) + dV([2*x*y]), V(2*x*y), V(((-x^3)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta1 - ETA1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().re[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (eta1 - ETA1).reduce()

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3)/y) dx), [0], V(((-x^3)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: eta1.omega0

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta1.omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V((x^5/y) dx) + dV(2*x*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lseta1.omega8[?7h[?12l[?25h[?25l[?7leta1.omega8[?7h[?12l[?25h[?25l[?7lceta1.omega8[?7h[?12l[?25h[?25l[?7loneta1.omega8[?7h[?12l[?25h[?25l[?7ldeta1.omega8[?7h[?12l[?25h[?25l[?7l_eta1.omega8[?7h[?12l[?25h[?25l[?7lpeta1.omega8[?7h[?12l[?25h[?25l[?7laeta1.omega8[?7h[?12l[?25h[?25l[?7lteta1.omega8[?7h[?12l[?25h[?25l[?7lceta1.omega8[?7h[?12l[?25h[?25l[?7lheta1.omega8[?7h[?12l[?25h[?25l[?7l(eta1.omega8[?7h[?12l[?25h[?25l[?7leta1.omega8[?7h[?12l[?25h[?25l[?7l(eta1.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(eta1.omega8).regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^8 + x^6 + 1)/(x^3*y)) dx) + dV(x*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(eta1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lE1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lT1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lA1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lsage: second_patch(ETA1.omega8).regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(x*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy/x)^3[?7h[?12l[?25h[?25l[?7l/y/x)^3[?7h[?12l[?25h[?25l[?7ly/x)^3[?7h[?12l[?25h[?25l[?7l.y/x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)^3[?7h[?12l[?25h[?25l[?7l.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy - v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l.y - v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCv - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l.v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y - C.v - (C.y/C.x)^3

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 C.y - C.v - (C.y/C.x)**Integer(3)

AttributeError: 'superelliptic' object has no attribute 'v'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y - C.v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7lv - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y - v - (C.y/C.x)^3

[?7h[?12l[?25h[?2004l[?7h0
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bash: syntax error near unexpected token `;'
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy.teichmuler() - v.teichmuler()[?7h[?12l[?25h[?25l[?7l.y.teichmuler() - v.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l ()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lv()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7lc()[?7h[?12l[?25h[?25l[?7lh()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7lb()[?7h[?12l[?25h[?25l[?7lu()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7lg()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ly).verschiebung()[?7h[?12l[?25h[?25l[?7l*).verschiebung()[?7h[?12l[?25h[?25l[?7lv).verschiebung()[?7h[?12l[?25h[?25l[?7l^).verschiebung()[?7h[?12l[?25h[?25l[?7l2).verschiebung()[?7h[?12l[?25h[?25l[?7l ).verschiebung()[?7h[?12l[?25h[?25l[?7l-).verschiebung()[?7h[?12l[?25h[?25l[?7l ).verschiebung()[?7h[?12l[?25h[?25l[?7lC).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ly).verschiebung()[?7h[?12l[?25h[?25l[?7l^).verschiebung()[?7h[?12l[?25h[?25l[?7l2).verschiebung()[?7h[?12l[?25h[?25l[?7l*).verschiebung()[?7h[?12l[?25h[?25l[?7lv).verschiebung()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=
[?7h[?12l[?25h[?25l[?7l
sage: C.y.teichmuller() - v.teichmuller()+ (C.y*v^2 - C.y^2*v).verschiebung() =
=

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l3.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller() - v.teichmuller()+ (C.y*v^2 - C.y^2*v).verschiebung() =
=

....: ( (C.y/C.x)^3).teichmuller()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller() - v.teichmuller()+ (C.y*v^2 - C.y^2*v).verschiebung() =
=

....: ( (C.y/C.x)^3).teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

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 (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l
(

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=

( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ld


=( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l
i

 =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ln =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l( =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().+ (C.y*v^2 - C.y^2*v).verschiebung().
d

ifn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ld+ (C.y*v^2 - C.y^2*v).verschiebung()
.

difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7li+ (C.y*v^2 - C.y^2*v).verschiebung(
)

.difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf+ (C.y*v^2 - C.y^2*v).verschiebung
(

).difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf+ (C.y*v^2 - C.y^2*v).verschiebun
g

().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ln+ (C.y*v^2 - C.y^2*v).verschiebu
n

g().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l(+ (C.y*v^2 - C.y^2*v).verschieb
u

ng().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l()+ (C.y*v^2 - C.y^2*v).verschie
b

ung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(). - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).verschi
e

bung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ld - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).versch
i

ebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7li - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).versc
h

iebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).vers
c

hiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).ver
s

chiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ln - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).ve
r

schiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l( - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).v
e

rschiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l() - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).
v

erschiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

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v

....: erschiebung().diffn() =( (C.y/C.x)^3).teichmuller().diffn()

[?7h[?12l[?25h[?2004l  Input In [4]
    C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v**Integer(2) - C.y**Integer(2)*v).verschiebung().diffn() =( (C.y/C.x)**Integer(3)).teichmuller().diffn()
    ^
SyntaxError: cannot assign to expression here. Maybe you meant '==' instead of '='?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).
v

....: erschiebung().diffn() =( (C.y/C.x)^3).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()= =( (C.y/C.x)^3).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=( (C.y/C.x)^3).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).
v

....: erschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()

[?7h[?12l[?25h[?2004l
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta1 - ETA1).reduce()[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+Cx)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x)^2*(C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^4 + 1)/(x^2*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l - ETA1[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

....: ebung())[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

ebung())[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

....: ebung())

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: ETA1 = C.crystalline_cohomology_basis()[0]

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v

[?7h[?12l[?25h[?2004l[?7h1/x^2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

....: ebung())[?7h[?12l[?25h[?25l[?7l(C.y/C.x)^2*(C.y/C.x).diffn()

 

 [?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).
v

....: erschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(C.y/C.x)^2*(C.y/C.x).diffn()

 [?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x)^2*(C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^4 + 1)/(x^2*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x)^2*(C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y*v^2 - C.y^2*v)

[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y*v^2 - C.y^2*v)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y*v^2 - C.y^2*v).coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

....: ebung())[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.h2expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lby[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lC)).mult_by_p()[?7h[?12l[?25h[?25l[?7l.)).mult_by_p()[?7h[?12l[?25h[?25l[?7lx)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l^).mult_by_p()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l-)).mult_by_p()[?7h[?12l[?25h[?25l[?7l2)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*).mult_by_p()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lC)).mult_by_p()[?7h[?12l[?25h[?25l[?7l.)).mult_by_p()[?7h[?12l[?25h[?25l[?7ly)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l^).mult_by_p()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l0)).mult_by_p()[?7h[?12l[?25h[?25l[?7l)).mult_by_p()[?7h[?12l[?25h[?25l[?7l-)).mult_by_p()[?7h[?12l[?25h[?25l[?7l1)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*).mult_by_p()[?7h[?12l[?25h[?25l[?7lC).mult_by_p()[?7h[?12l[?25h[?25l[?7l.).mult_by_p()[?7h[?12l[?25h[?25l[?7ld).mult_by_p()[?7h[?12l[?25h[?25l[?7lx).mult_by_p()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
sage: om1 = v.teichmuller().diffn() + ((C.x)^(-2)*(C.y)^(-1)*C.dx).mult_by_p() 
+

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 [?7h[?12l[?25h[?25l[?7l
+

....: [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = v.teichmuller().diffn() + ((C.x)^(-2)*(C.y)^(-1)*C.dx).mult_by_p() 
+

....: (C.y/C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004l
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 om1 = v.teichmuller().diffn() + ((C.x)**(-Integer(2))*(C.y)**(-Integer(1))*C.dx).mult_by_p() +(C.y/C.x**Integer(3)).verschiebung().diffn()

AttributeError: 'superelliptic_form' object has no attribute 'mult_by_p'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA == B[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: A = C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.dx[?7h[?12l[?25h[?25l[?7l.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: A.h2.expansion_at_infty()

  A.cartier               A.expansion_at_infty    A.jth_component         
 

  A.coordinates           A.form                  A.reduce                
 

  A.curve                 A.is_regular_on_U0      A.reduce2               
>

  A.expansion             A.is_regular_on_Uinfty  A.regular_form          
 

 [?7h[?12l[?25h[?25l[?7lcartier

 A.cartier              







 <unknown> [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

 A.cartier               A.expansion_at_infty   [?7h[?12l[?25h[?25l[?7ljth_component

 A.expansion_at_infty    A.jth_component        [?7h[?12l[?25h[?25l[?7lresidue

 expansion_at_inftyjth_component     residue       

 frm       reducesrre_duality_pairing 

<is_rgular_on_U0reduce2         vrshiebung 

 is_regular_on_Uinftyregular_form                                 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ljth_component

 A.jth_component         A.residue              [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

 A.expansion_at_infty    A.jth_component        [?7h[?12l[?25h[?25l[?7lcartier

 cartier           expansion_at_inftyjth_component 

 cordinatesform  rduce                

 curv           is_regular_on_U0rdue2     >

 expansion           is_regular_on_Uinfty A.regular_form          
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lby[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(A)

[?7h[?12l[?25h[?2004l[?7hV((x^2) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(A)[?7h[?12l[?25h[?25l[?7lA = C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = v.teichmuller().diffn() + ((C.x)^(-2)*(C.y)^(-1)*C.dx).mult_by_p() 
+

....: (C.y/C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( +
(

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.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7ly((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y
/

C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l_((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.
y

/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7lp((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C
.

y/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = v.teichmuller().diffn() + mult_by_p((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C
.

....: y/C.x^3).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lta1[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1.omega8 == om1

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega8 == om1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

....: ebung())[?7h[?12l[?25h[?25l[?7l-ETA1

 

 [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lTA1[?7h[?12l[?25h[?25l[?7lsage: eta1 - ETA1

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3)/y) dx) + dV([2*x*y]), V(2*x*y), V(((-x^3)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta1 - ETA1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).reduce()[?7h[?12l[?25h[?25l[?7l().reduce()[?7h[?12l[?25h[?25l[?7lsage: (eta1 - ETA1).reduce()

[?7h[?12l[?25h[?2004l[?7h(V(((-x^3)/y) dx), [0], V(((-x^3)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(ETA1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.y)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x^3*C.y.diffn())

[?7h[?12l[?25h[?2004l[?7h((-1)/(x^3*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x^3*C.y.diffn())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l+_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^3*C.y.diffn()).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.diffn()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: (C.x^3*C.y.diffn()).expansion_at_infty(prec = 30)

[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + t^10 + t^18 + O(t^24)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lta2[?7h[?12l[?25h[?25l[?7lsage: ETA2 - eta2

[?7h[?12l[?25h[?2004l[?7h( + V(((x^8 - x^6 + 1)/y) dx) + dV([(x^4 + x^2 + 1)*y]), V((x^4 + x^2 + 1)*y), V(((x^8 - x^6 + 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 - eta2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ETA2 - eta2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (ETA2 - eta2).reduce()

[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l=(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7lsage: A = (ETA2 - eta2).reduce()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: A = A.omega8.omega

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = A.omega8.omega[?7h[?12l[?25h[?25l[?7l.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: A.expansion

 A.expansion         

 A.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 A.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 A.expansion         

 A.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-16 + t^-8 + O(t^-6)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lA.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: A.expansion_at_infty(prec = 30)

[?7h[?12l[?25h[?2004l[?7ht^-16 + t^-8 + t^-4 + 1 + 2*t^4 + 2*t^12 + O(t^14)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lA.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lir()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).verschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7leC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7loC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lnC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ldC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l_C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lpC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ltC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lhC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l(C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.de_rham_basis()[1].omega8)

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [34], in <cell line: 1>()
----> 1 u

NameError: name 'u' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l = C.one/C.x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: -u*v.diffn()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(ETA2).coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l(ETA2).coordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(ETA2).coordinates()

[?7h[?12l[?25h[?2004l(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [37], in <cell line: 1>()
----> 1 autom(ETA2).coordinates()

File <string>:84, in coordinates(self, basis)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = A.omega8.omega[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx*y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l/x*y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx*y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x*y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l/x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7lx^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: A.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: A.expansion_at_infty(prec = 30)

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + t^12 + t^16 + t^18 + 2*t^22 + O(t^28)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[1][?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lc = C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lr = C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lys= C.crystalline_chmlogy_bais()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Bcrys = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(ETA2).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB) - B - A[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[p[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(Bcrys[1]).coordinates(basis = Bcrys)

[?7h[?12l[?25h[?2004l(1, 1)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 autom(Bcrys[Integer(1)]).coordinates(basis = Bcrys)

File <string>:85, in coordinates(self, basis)

File <string>:56, in coordinates(self)

File <string>:93, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: Bcrys = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lsage: autom(Bcrys[1]).coordinates(basis = Bcrys)

[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
(1, 1)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((x + 1)/(x*y - y)) dx, 0, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
coordinates of form self ((x + 1)/(x*y - y)) dx
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 autom(Bcrys[Integer(1)]).coordinates(basis = Bcrys)

File <string>:87, in coordinates(self, basis)

File <string>:56, in coordinates(self)

File <string>:94, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: Bcrys = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAautom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lAautom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l=autom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lsage: AA = autom(Bcrys[1]).coordinates(basis = Bcrys)

[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
(1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA = autom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: AA

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AA.reduce()

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [0],  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA.reduce()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: AA

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [0],  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.reduce()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loA.omega0.omega[?7h[?12l[?25h[?25l[?7lmA.omega0.omega[?7h[?12l[?25h[?25l[?7l A.omega0.omega[?7h[?12l[?25h[?25l[?7l-A.omega0.omega[?7h[?12l[?25h[?25l[?7l=A.omega0.omega[?7h[?12l[?25h[?25l[?7l A.omega0.omega[?7h[?12l[?25h[?25l[?7lA.omega0.omega[?7h[?12l[?25h[?25l[?7lA.omega0.omega[?7h[?12l[?25h[?25l[?7lA.omega0.omega[?7h[?12l[?25h[?25l[?7l=A.omega0.omega[?7h[?12l[?25h[?25l[?7l A.omega0.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = AA.omega0.omega

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AA.omega0.omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AA.omega0.omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h((x + 1)/(x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(Bcrys[1])

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([((x^6 + 2*x^5 + 2*x^3 + x^2 + x)/(x^2 + x + 1))*y]), [(2/(x + 1))*y] + V((x^4 + x^3 + x^2)*y), [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 - x^2 + 1)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: autom(Bcrys[1]) - Bcrys[0] - Bcrys[1]

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7lrautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l=autom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: rr = autom(Bcrys[1]) - Bcrys[0] - Bcrys[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lcr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: Bcrys[1]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys[1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loBcrys[1].omega0[?7h[?12l[?25h[?25l[?7lmBcrys[1].omega0[?7h[?12l[?25h[?25l[?7l Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l=Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = Bcrys[1].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom1).frobenius()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = Bcrys[1].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: om0 = Bcrys[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7l = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lto[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom1).frobenius()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(om1)

[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([((x^6 + 2*x^5 + 2*x^3 + x^2 + x)/(x^2 + x + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: autom(om1) - om1 - om0

[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lomega.expansionat_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: om1.omega

[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.omega.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys[1][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[1][?7h[?12l[?25h[?25l[?7lsage: Bcrys[1]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 - C.x.teichmuller()*C.y().teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [72], in <cell line: 1>()
----> 1 om1 - C.x.teichmuller()*C.y().teichmuller().diffn()

TypeError: 'superelliptic_function' object is not callable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 - C.x.teichmuller()*C.y().teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 - C.x.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.de_rha_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: autom(C.x.teichmuller().diffn())

[?7h[?12l[?25h[?2004l[?7h[1] d[x]dV([x^2 + x])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom1) - om1 - om0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1) - om1 - om0[?7h[?12l[?25h[?25l[?7lsage: autom(om1) - om1 - om0

[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 - C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omegargular_fom()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x] d[y] + V(((x^8 - x^6 + 1)/y) dx) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7lx^8 - x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8 - x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x^8 - x^6)[?7h[?12l[?25h[?25l[?7l (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l=(x^8 - x^6)[?7h[?12l[?25h[?25l[?7l (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: g = (x^8 - x^6)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

[?7h[?12l[?25h[?2004l[?7h2*x^7 + x^6 + 2*x^5 + x^4 + x^2 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = (x^8- x^6)[?7h[?12l[?25h[?25l[?7lom0.regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lautom(om1) - m1 - om0[?7h[?12l[?25h[?25l[?7lom1.regular_frm()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lg = (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l(x+1) -g[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = (x^8- x^6)[?7h[?12l[?25h[?25l[?7lom0.regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lautom(om1) - m1 - om0[?7h[?12l[?25h[?25l[?7l(C.x.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7l(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAautom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l=autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = autom(om1) - om1 - om0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys[1][?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift_form0(C.x/C.y*C.dx)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.x^2 + C.x)*C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lbu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(().verschiebung()[?7h[?12l[?25h[?25l[?7l(()).verschiebung()[?7h[?12l[?25h[?25l[?7l*).verschiebung()[?7h[?12l[?25h[?25l[?7lC).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ly).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ld).verschiebung()[?7h[?12l[?25h[?25l[?7li).verschiebung()[?7h[?12l[?25h[?25l[?7lf).verschiebung()[?7h[?12l[?25h[?25l[?7lf).verschiebung()[?7h[?12l[?25h[?25l[?7ln).verschiebung()[?7h[?12l[?25h[?25l[?7l(().verschiebung()[?7h[?12l[?25h[?25l[?7l(()).verschiebung()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l*)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l7)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l6)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l5)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l4)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l2)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l*)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l3)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l2)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l2)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l*)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = ((C.x^2 + C.x)*C.y^2*C.y.diffn()).verschiebung() + ((2*C.x^7 + C.x^6 + C.x^5 + C.x^4 + 2*C.x^3+C.x^2+2*C.x)*C.y.diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l= B[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A == B

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA == B[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.cartier()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [83], in <cell line: 1>()
----> 1 A.cartier()

AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7locartier()[?7h[?12l[?25h[?25l[?7lmcartier()[?7h[?12l[?25h[?25l[?7lecartier()[?7h[?12l[?25h[?25l[?7lgcartier()[?7h[?12l[?25h[?25l[?7lacartier()[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lsage: A.omega.cartier()

[?7h[?12l[?25h[?2004l[?7h((x + 1)/(x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.omega.cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.omega.cartier()[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^5 + x^4 + x^2 + x)/(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l.(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lq(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lu(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lo(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l_(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lr(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7le(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lm(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: (x^5 + x^4 + x^2 + x).quo_rem(x^2 + x + 1)

[?7h[?12l[?25h[?2004l[?7h(x^3 + 2*x + 2, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u

[?7h[?12l[?25h[?2004l[?7h1/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: u.expansion

 u.expansion         

 u.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 u.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 u.expansion         

 u.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: u.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + O(t^22)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lu.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.omega.cartier()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lsage: A.omega.cartier()

[?7h[?12l[?25h[?2004l[?7h((x + 1)/(x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.omega.cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.omega.cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx.egular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)C.dx[?7h[?12l[?25h[?25l[?7l.)C.dx[?7h[?12l[?25h[?25l[?7ly)C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l1C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm(C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l=(C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = (C.y)^(-1)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7limport itertools.product as product[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: inv_cartier(om)

[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linv_cartier(om)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linv_cartier(om)[?7h[?12l[?25h[?25l[?7lninv_cartier(om)[?7h[?12l[?25h[?25l[?7lvinv_cartier(om)[?7h[?12l[?25h[?25l[?7l_inv_cartier(om)[?7h[?12l[?25h[?25l[?7lcinv_cartier(om)[?7h[?12l[?25h[?25l[?7lainv_cartier(om)[?7h[?12l[?25h[?25l[?7lrinv_cartier(om)[?7h[?12l[?25h[?25l[?7ltinv_cartier(om)[?7h[?12l[?25h[?25l[?7linv_cartier(om)[?7h[?12l[?25h[?25l[?7leinv_cartier(om)[?7h[?12l[?25h[?25l[?7lrinv_cartier(om)[?7h[?12l[?25h[?25l[?7l(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: inv_cartier(inv_cartier(om))

[?7h[?12l[?25h[?2004l[?7h((x^12 - x^10 - x^6 + x^4)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linv_cartier(inv_cartier(om))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7linv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l inv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l=inv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l inv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ii = inv_cartier(inv_cartier(om))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l/dx[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy) C.dx[?7h[?12l[?25h[?25l[?7l.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l. x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii

[?7h[?12l[?25h[?2004l[?7h((-x^14 - x^13 + x^11 + x^10 + x^8 + x^7 - x^5 - x^4 - x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lii = inv_cartier(inv_cartier(om))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: ii.is_regular_on_U

 ii.is_regular_on_U0    

 ii.is_regular_on_Uinfty





 [?7h[?12l[?25h[?25l[?7l0

 ii.is_regular_on_U0    



 <unknown> [?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ii.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lii.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - i).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier()

[?7h[?12l[?25h[?2004l[?7h((-x^4 + x^3 + x^2 + 1)/(x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier().cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l i).cartier()[?7h[?12l[?25h[?25l[?7l+ i).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier()

[?7h[?12l[?25h[?2004l[?7h((x^4 - x^3 - x^2 - x + 1)/(x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-().cartier()[?7h[?12l[?25h[?25l[?7l+()[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7lsage: x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(0, 9):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: G = x^3 + x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG = x^3 + x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: G.

  G.abs                         G.all_roots_in_interval       G.base_ring                   G.change_variable_name        G.compose_trunc                

  G.adams_operator              G.any_root                    G.cartesian_product           G.coefficients                G.composed_op                  

  G.add_bigoh                   G.args                        G.category                    G.complex_roots               G.constant_coefficient        >

  G.additive_order              G.base_extend                 G.change_ring                 G.compose_power               G.content_ideal                

 [?7h[?12l[?25h[?25l[?7labs

 G.abs                        







 <unknown> [?7h[?12l[?25h[?25l[?7lll_roots_in_interval

 G.abs                         G.all_roots_in_interval      [?7h[?12l[?25h[?25l[?7lbase_ring

 G.all_roots_in_interval       G.base_ring                  [?7h[?12l[?25h[?25l[?7lchange_variable_name

 G.base_ring                   G.change_variable_name       [?7h[?12l[?25h[?25l[?7lompose_tunc

 G.change_variable_name        G.compose_trunc              [?7h[?12l[?25h[?25l[?7lycltomic_part

 ll_roots_in_intervalbase_ring            change_variable_nameompose_tunc       ycltomic_part

 ny_rot      cartesian_productoefficients     mposed_op degree     

<rgs     categoryomplex_rootsnstant_cefficientdeomiator         

 base_extend   chang_rigompose_powerntentidealderivaive   [?7h[?12l[?25h[?25l[?7ldit

base_ring            change_variable_nameompose_tunc       ycltomic_partdit           

cartesian_productoefficients     mposed_op degree     iff  

categoryomplex_rootsnstant_cefficientdeomiator         iffereniate

chang_rigompose_powerntentidealderivaive   iscrimnant[?7h[?12l[?25h[?25l[?7lspersion

change_variable_nameompose_tunc       ycltomic_partdit           spersion

oefficients     mposed_op degree     iff  spersion_set

omplex_rootsnstant_cefficientdeomiator         iffereniatevides      

ompose_powerntentidealderivaive   iscrimnantump        [?7h[?12l[?25h[?25l[?7lums

ompose_tunc       ycltomic_partdit           spersionums     

mposed_op degree     iff  spersion_seteuclidean_degree

nstant_cefficientdeomiator         iffereniatevides      exponnts

ntentidealderivaive   iscrimnantump        factor[?7h[?12l[?25h[?25l[?7lgcd

ycltomic_partdit           spersionums     gcd  

degree     iff  spersion_seteuclidean_degreeget_cparent     

deomiator         iffereniatevides      exponntsglobal_height

derivaive   iscrimnantump        factorgradient[?7h[?12l[?25h[?25l[?7lhamming_weight

dit           spersionums     gcd  hamming_weight

iff  spersion_seteuclidean_degreeget_cparent     hasyclotomic_factor

iffereniatevides      exponntsglobal_heighthomogenize   

iscrimnantump        factorgradientintegral[?7h[?12l[?25h[?25l[?7linversemod

spersionums     gcd  hamming_weightinversemod   

spersion_seteuclidean_degreeget_cparent     hasyclotomic_factorinverse_f_unit      

vides      exponntsglobal_heighthomogenize   inverse_sries_trunc

ump        factorgradientintegrals_constant[?7h[?12l[?25h[?25l[?7lhammingweight

 G.hamming_weight              G.inverse_mod                [?7h[?12l[?25h[?25l[?7ls_cyclotomic_factor

 G.hamming_weight             

 G.has_cyclotomic_factor      [?7h[?12l[?25h[?25l[?7lomogenize



 G.has_cyclotomic_factor      

 G.homogenize                 [?7h[?12l[?25h[?25l[?7linteral





 G.homogenize                 

 G.integral                   [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: G.integral()

[?7h[?12l[?25h[?2004l[?7hx^4 + 2*x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lG.integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG.integral()[?7h[?12l[?25h[?25l[?7l = x^3 + x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: G = x^3 + x + x^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lG = x^3 + x + x^2[?7h[?12l[?25h[?25l[?7l.integral()[?7h[?12l[?25h[?25l[?7lsage: G.integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [109], in <cell line: 1>()
----> 1 G.integral()

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
   3992 cdef Py_ssize_t n
   3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
   3996 return S(p)

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = (C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((x^5 + x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((x^5 + x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: om.int() - (C.y/C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [115], in <cell line: 1>()
----> 1 om.int() - (C.y/C.x)

File <string>:26, in __sub__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: om = (C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: om.int() - (C.y/C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [118], in <cell line: 1>()
----> 1 om.int() - (C.y/C.x)

File <string>:199, in int(self)

File <string>:19, in __add__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [119], in <cell line: 1>()
----> 1 om.int()

File <string>:199, in int(self)

File <string>:19, in __add__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: om = (C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lcartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.carier()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [122], in <cell line: 1>()
----> 1 om.carier()

AttributeError: 'superelliptic_form' object has no attribute 'carier'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.carier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l.carier()[?7h[?12l[?25h[?25l[?7ltier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l.carier()[?7h[?12l[?25h[?25l[?7ltier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: om.int() - (C.y/C.x)

[?7h[?12l[?25h[?2004l[?7h((x^5 + 2*x^2 + x + 1)/(x^3 + 2*x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (om.int() - (C.y/C.x)).pth_root()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [126], in <cell line: 1>()
----> 1 (om.int() - (C.y/C.x)).pth_root()

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis[1].omega8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om = C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linn[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = C.y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.y.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((x^3 + x)/(x^2 + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: om.int() - C.y

[?7h[?12l[?25h[?2004l[?7h((x^3 + 2*x^2 + x + 1)/(x^2 + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - C.y[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om.int() - C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (om.int() - C.y).pth_root()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [132], in <cell line: 1>()
----> 1 (om.int() - C.y).pth_root()

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - C.y[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn()

[?7h[?12l[?25h[?2004l[?7h(x^5/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = C.y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.y.diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7l = C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7l(om.int() - C.y).pth_root()[?7h[?12l[?25h[?25l[?7lom.int() - C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l = C.y.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = C.dx[?7h[?12l[?25h[?25l[?7l(om.int() - (C.y/C.x)).pth_root()[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: om = (C.y/C.x).diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().diffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^2 - 1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((x^4 + 1)/(x^5 + x^3 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: om = C.x*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.x*C.y[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.difn()[?7h[?12l[?25h[?25l[?7lmom.difn()[?7h[?12l[?25h[?25l[?7l om.difn()[?7h[?12l[?25h[?25l[?7l=om.difn()[?7h[?12l[?25h[?25l[?7l om.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = om.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((x^5 + x^3)/(x^4 + x^2 + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l().diffn() == om[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn()

[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8(aux)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7losition_g0_g8(aux)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lin)[?7h[?12l[?25h[?25l[?7lint)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(om.int())

[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/(x^4 + x^2 + 1))*y, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

















 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Input In [1] in <cell line: 1>
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:21 in <module>

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:22
    if self.dx = _sage_const_0 *C.x and self.y = _sage_const_0 *C.x:
       ^
SyntaxError: cannot assign to attribute here. Maybe you meant '==' instead of '='?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = (x^8- x^6)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7log.difn()[?7h[?12l[?25h[?25l[?7lmg.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l=g.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.difn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().diffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 om.int()

File <string>:21, in int(self)

AttributeError: 'superelliptic_regular_form' object has no attribute 'fct_field'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 om = om.regular_form()

AttributeError: 'superelliptic_regular_form' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 om.int()

File <string>:28, in int(self)

ValueError: not enough values to unpack (expected 2, got 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lself.fct_field = Fxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lselfFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om.int() - C.y).pth_root()[?7h[?12l[?25h[?25l[?7lx^5 + x^4 + x^2 + x).quo_rem(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^6*y^7).exponents()

[?7h[?12l[?25h[?2004l[?7h[(6, 7)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l,(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l (x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7lj(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l (x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l=(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l (x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: i, j = (x^6*y^7).exponents()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 om.int()

File <string>:30, in int(self)

File <string>:30, in int(self)

    [... skipping similar frames: int at line 30 (3 times)]

File <string>:30, in int(self)

File <string>:29, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
   1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
-> 1739     return coercion_model.bin_op(left, right, truediv)
   1740 
   1741 try:

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [27], in <cell line: 1>()
----> 1 om.int()

File <string>:30, in int(self)

File <string>:30, in int(self)

    [... skipping similar frames: int at line 30 (3 times)]

File <string>:30, in int(self)

File <string>:29, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
   1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
-> 1739     return coercion_model.bin_op(left, right, truediv)
   1740 
   1741 try:

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 om.int()

File <string>:32, in int(self)

File <string>:32, in int(self)

    [... skipping similar frames: int at line 32 (3 times)]

File <string>:32, in int(self)

File <string>:31, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
   1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
-> 1739     return coercion_model.bin_op(left, right, truediv)
   1740 
   1741 try:

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 - x^12 - x^10) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7hx^19 + 2*x^17 + 2*x^13 + x^11
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(0, 9):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l()o[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7log.difn()[?7h[?12l[?25h[?25l[?7lmg.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l=g.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l- C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lnm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.int()[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpip install -U sage[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (2) dy
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [46], in <cell line: 1>()
----> 1 om.int()

File <string>:23, in int(self)

AttributeError: 'superelliptic_regular_form' object has no attribute 'y'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((2*x^2 + 2)/(x^4 + x^2 + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7legular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (2) dy
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 om.int()

File <string>:36, in int(self)

NameError: name 'dy' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (2) dy
m dx 1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 om.int()

File <string>:38, in int(self)

ValueError: not enough values to unpack (expected 2, got 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (2) dy
m dx 1
int(self) ((1/(x^2 + 2))*y + 2) dy
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1008 # now try calling the base ring's __call__ methods
-> 1009 element = self.base_ring()(element)
   1010 _p = p_NSet(sa2si(element,_ring), _ring)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
   1691 for f in self.__list:
-> 1692     x = f._call_(x)
   1693 return x

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
  12065 """
> 12066 cpdef Element _call_(self, x):
  12067     """

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
  12090 else:
> 12091     raise TypeError("not a constant polynomial")
  12092 

TypeError: not a constant polynomial

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [62], in <cell line: 1>()
----> 1 om.int()

File <string>:40, in int(self)

File <string>:35, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1011         return new_MP(self,_p)
   1012     except (TypeError, ValueError):
-> 1013         raise TypeError("Could not find a mapping of the passed element to this ring.")
   1014 
   1015 def _repr_(self):

TypeError: Could not find a mapping of the passed element to this ring.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l - C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (2) dy
m dy 1
int(self) (0) dy
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [67], in <cell line: 1>()
----> 1 om.int()

File <string>:40, in int(self)

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lg = - C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (2) dy
m dy 1
int(self) (0) dy
[?7h2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [76], in <cell line: 1>()
----> 1 om.int()

File <string>:32, in int(self)

File <string>:32, in int(self)

    [... skipping similar frames: int at line 32 (3 times)]

File <string>:32, in int(self)

File <string>:31, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
   1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
-> 1739     return coercion_model.bin_op(left, right, truediv)
   1740 
   1741 try:

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= om.regular_form()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l-uteichmullr()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dx y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dx 1
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
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m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 om.int()

File <string>:33, in int(self)

File <string>:33, in int(self)

    [... skipping similar frames: int at line 33 (6 times)]

File <string>:42, in int(self)

    [... skipping similar frames: int at line 33 (1 times)]

File <string>:42, in int(self)

    [... skipping similar frames: int at line 33 (159 times), int at line 42 (159 times)]

File <string>:33, in int(self)

File <string>:42, in int(self)

File <string>:27, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    989     else:
    990         element = element.replace("^","**")
--> 991         element = eval(element, d, {})
    992 except (SyntaxError, NameError):
    993     raise TypeError("Could not find a mapping of the passed element to this ring.")

File <string>:1, in <module>

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^12*y
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (x^13) dy
m dx x^4
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^2 + 2) dx + (x^13) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^13) dy
m dx y
int(self) ((x^16 + 2*x^10)*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^6
int(self) (2*x^10*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2 + 2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx 1
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx y
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^12*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
m dx x^2
m dy x^13
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx y
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^16*y
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^10*y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^12*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^12*y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^10*y
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^2
m dy x
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx x^10*y
int(self) ((x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + 2*x^11) dy
m dx x^12*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^16*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^12*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^18*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^18*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^10*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17) dy
m dx y
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^12*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx y
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^12*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx y
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^12*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^18*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^10*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^12*y
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^10*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^12*y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^16*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^10*y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx x^12*y
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^16*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^18*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^16*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^18*y
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^12*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^18*y
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^10*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^16*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^12*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + 2*x^11) dy
m dx x^12*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^16*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
m dx x^2
m dy x^13
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx y
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^12*y
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^10*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [88], in <cell line: 1>()
----> 1 om.int()

File <string>:34, in int(self)

File <string>:34, in int(self)

    [... skipping similar frames: int at line 34 (5 times)]

File <string>:43, in int(self)

    [... skipping similar frames: int at line 34 (2 times)]

File <string>:43, in int(self)

    [... skipping similar frames: int at line 34 (229 times), int at line 43 (229 times)]

File <string>:34, in int(self)

File <string>:43, in int(self)

File <string>:42, in int(self)

File <string>:51, in __sub__(self, other)

File <string>:224, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1198 # Now coerce to a common parent and do the operation there
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:
   1202     self._record_exception()

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1309 x_map, y_map = coercions
   1310 if x_map is not None:
-> 1311     x_elt = (<Map>x_map)._call_(x)
   1312 else:
   1313     x_elt = x

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    417 w = {remove_from_tuple(e, ind): val
    418      for e, val in self.dict().iteritems() if not e[ind]}
--> 419 v = [B(w)]  # coefficients that don't involve var
    420 z = var
    421 for i in range(1,d+1):

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:462, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    460     if x.type() != 't_POL':
    461         x = x.Polrev()
--> 462 elif isinstance(x, FiniteRingElement):
    463     try:
    464         return self(x.polynomial())

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lnt()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [92], in <cell line: 1>()
----> 1 om.int()

File <string>:26, in int(self)

NameError: name 'random_choice' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l^[[A[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [97], in <cell line: 1>()
----> 1 om.int()

File <string>:38, in int(self)

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/random.py:378, in Random.choice(self, seq)
    376 """Choose a random element from a non-empty sequence."""
    377 # raises IndexError if seq is empty
--> 378 return seq[self._randbelow(len(seq))]

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form().int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:60, in __mul__(self, other)

File <string>:14, in __init__(self, C, g)

File <string>:220, in reduction(C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
    630         raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
    634 # At this point, we have only handled the "names" keyword if it was
    635 # needed. Since we know the variable names, it would logically be
    636 # an error to specify an additional "names" keyword. However,
   (...)
    639 # and we allow this for historical reasons. However, the names
    640 # must be consistent!

File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
    899 
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
    901     r"""

File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
    992     # Convert names to strings and strip whitespace
--> 993     names = [str(x).strip() for x in names]
    994 else:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [100], in <cell line: 1>()
----> 1 om = g.diffn().regular_form().int()

File <string>:35, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 35 (4 times)]

File <string>:44, in int(self)

    [... skipping similar frames: int at line 35 (1 times)]

File <string>:44, in int(self)

    [... skipping similar frames: int at line 35 (219 times), int at line 44 (219 times)]

File <string>:35, in int(self)

File <string>:44, in int(self)

File <string>:34, in int(self)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Input In [101] in <cell line: 1>
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:21 in <module>

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:30
    print('m dx', m)
    ^
IndentationError: expected an indented block after 'for' statement on line 29

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [102], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:21, in <module>

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

    [... skipping similar frames: sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times), sage.structure.element.Element.__mul__ at line 1528 (3 times), __rmul__ at line 43 (2 times)]

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:41, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:70, in __rmul__(self, constant)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form().int()

[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dx y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dx 1
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [105], in <cell line: 1>()
----> 1 om = g.diffn().regular_form().int()

File <string>:35, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 35 (6 times)]

File <string>:44, in int(self)

    [... skipping similar frames: int at line 35 (1 times)]

File <string>:44, in int(self)

    [... skipping similar frames: int at line 35 (70 times), int at line 44 (70 times)]

File <string>:35, in int(self)

File <string>:44, in int(self)

File <string>:34, in int(self)

File <string>:82, in __pow__(self, exp)

File <string>:7, in __init__(self, C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
    629     except KeyError:
    630         raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
    634 # At this point, we have only handled the "names" keyword if it was
    635 # needed. Since we know the variable names, it would logically be
    636 # an error to specify an additional "names" keyword. However,
   (...)
    639 # and we allow this for historical reasons. However, the names
    640 # must be consistent!
    641 if "names" in kwds:

File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
    898         return dir_with_other_class(self, self.category().parent_class)
    899 
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
    901     r"""
    902     Return a tuple of strings of variable names of length ngens given

File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
    991 if isinstance(names, (tuple, list)):
    992     # Convert names to strings and strip whitespace
--> 993     names = [str(x).strip() for x in names]
    994 else:
    995     # Interpret names as string and convert to tuple of strings

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form(); om

[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7hx^19 + 2*x^17 + 2*x^13 + x^11
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10) dx
m dx x^16
int(self) (2*x^12 + 2*x^10) dx
m dx x^12
int(self) (2*x^10) dx
m dx x^10
int(self) (0) dy
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [115], in <cell line: 1>()
----> 1 om.int()

File <string>:35, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 35 (1 times)]

File <string>:35, in int(self)

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form(); om

[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10) dx
m dx x^16
int(self) (2*x^12 + 2*x^10) dx
m dx x^12
int(self) (2*x^10) dx
m dx x^10
int(self) (0) dy
[?7hx^19 + 2*x^17 + 2*x^13 + x^11
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g - om.int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10) dx
m dx x^16
int(self) (2*x^12 + 2*x^10) dx
m dx x^12
int(self) (2*x^10) dx
m dx x^10
int(self) (0) dy
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - om.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lnm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form(); om

[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (2*x^6 + 2*x^4 + 2*x^2) dy
m dy x^6
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [123], in <cell line: 1>()
----> 1 om.int()

File <string>:44, in int(self)

File <string>:44, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 44 (1 times)]

File <string>:35, in int(self)

    [... skipping similar frames: int at line 44 (84 times), int at line 35 (84 times)]

File <string>:44, in int(self)

File <string>:35, in int(self)

File <string>:43, in int(self)

File <string>:52, in __sub__(self, other)

File <string>:14, in __init__(self, C, g)

File <string>:223, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    409 # Make polynomial ring over all variables except var.
    410 S = R.base_ring()[tuple(Z)]
--> 411 ring = S[var]
    412 if not self:
    413     return ring(0)

File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
   1273         except AttributeError:
   1274             return self.list()[n]
-> 1275     return meth(n)
   1276 
   1277 #########################################################################

File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
   1173 # 2. Otherwise, try to return a polynomial ring
   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:561, in PolynomialRing(base_ring, *args, **kwds)
    557 names = None  # Unknown variable names
    559 # Use a single-variate ring by default unless the "singular"
    560 # implementation is asked.
--> 561 multivariate = kwds.get("implementation") == "singular"
    563 # Check specifically for None because it is an easy mistake to
    564 # make and Integer(None) returns 0, so we wouldn't catch this
    565 # otherwise.
    566 if any(arg is None for arg in args):

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l2*(C.x.teichmuller)).diffn(), 2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (2*x^4 + 2*x^2).quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(2*x, x^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*x^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(2*x^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7lm(2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l (2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l=(2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l (2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2) dy[?7h[?12l[?25h[?25l[?7l.x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()* dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldy[?7h[?12l[?25h[?25l[?7lCdy[?7h[?12l[?25h[?25l[?7l.dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = (2*C.x^4 + 2*C.x^2)*C.y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (2*C.x^4 + 2*C.x^2)*C.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((x^6 + x^2)/(x^4 + x^2 + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller.diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).verschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y*C.y.diffn()

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7l.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lfrobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om1.form() == om

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lC))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lC))[?7h[?12l[?25h[?25l[?7l.))[?7h[?12l[?25h[?25l[?7lx))[?7h[?12l[?25h[?25l[?7l^))[?7h[?12l[?25h[?25l[?7l3))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l+))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lC))[?7h[?12l[?25h[?25l[?7l.))[?7h[?12l[?25h[?25l[?7lx))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2 = (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 = (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om2 == om1

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [138], in <cell line: 1>()
----> 1 om2 == om1

File <string>:12, in __eq__(self, other)

AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 == om1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 == om

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l om[?7h[?12l[?25h[?25l[?7l om[?7h[?12l[?25h[?25l[?7l- om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 - om

[?7h[?12l[?25h[?2004l[?7h((x^6 - x^3*y - x^2 - x*y)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 - om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om2 - om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (om2 - om).regular_form()

[?7h[?12l[?25h[?2004l[?7h((2*x^3 + 2*x)*y + x^6 + 2*x^2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.diffn().regular_form()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.diffn().regular_form()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [145], in <cell line: 1>()
----> 1 g.regular_form()

AttributeError: 'superelliptic_function' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldregular_form()[?7h[?12l[?25h[?25l[?7liregular_form()[?7h[?12l[?25h[?25l[?7lfregular_form()[?7h[?12l[?25h[?25l[?7lfregular_form()[?7h[?12l[?25h[?25l[?7lnregular_form()[?7h[?12l[?25h[?25l[?7l(regular_form()[?7h[?12l[?25h[?25l[?7l()regular_form()[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().int()

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7ldiffn().regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 - om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((2*x^8 + 2)/(x^4 + x^2 + 1))*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7legular_form()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr_form()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form()

[?7h[?12l[?25h[?2004l[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form().int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [155], in <cell line: 1>()
----> 1 om.regular_form().form().int()

File <string>:199, in int(self)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
   3992 cdef Py_ssize_t n
   3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
   3996 return S(p)

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form().int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l.diffn().int()[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l().form()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7l == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lregular_form().form() == om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l om[?7h[?12l[?25h[?25l[?7l om[?7h[?12l[?25h[?25l[?7l- om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() - om

[?7h[?12l[?25h[?2004l[?7h((x^21 - x^18*y - x^17 - x^16*y - x^15 + x^12*y + x^11 + x^10*y - x^6*y + x^6 - x^4*y + x^4 - x^3 - x^2*y + x^2 + x + 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() - om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form().form() - om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form()

[?7h[?12l[?25h[?2004l[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: lo

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 lo

NameError: name 'lo' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: g = C.x*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lfn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.reular_form().form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lar_form().form()[?7h[?12l[?25h[?25l[?7l() - om[?7h[?12l[?25h[?25l[?7l== om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lg = C.x*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l() - om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7l().form() == om[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form()

[?7h[?12l[?25h[?2004l[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form()

[?7h[?12l[?25h[?2004lif fct.denominator() == y:
if fct.denominator() == 1:
[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form()

[?7h[?12l[?25h[?2004lif fct.denominator() == y:
fct, fct.numerator() x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1 x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1
if fct.denominator() == 1:
[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l() == om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

[?7h[?12l[?25h[?2004lif fct.denominator() == y:
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().form() == om[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^16
int(self) (2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^12
int(self) (2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^10
int(self) (2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx 1
int(self) (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dy x^6
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File <string>:222, in reduction(C, g)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 om.regular_form().int()

File <string>:35, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 35 (3 times)]

File <string>:44, in int(self)

File <string>:44, in int(self)

    [... skipping similar frames: int at line 35 (124 times), int at line 44 (124 times)]

File <string>:35, in int(self)

File <string>:44, in int(self)

File <string>:34, in int(self)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.de_rham_basis()[1].omega8)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: om = superelliptic

 superelliptic                  superelliptic_drw/             superelliptic_form             superelliptic_regular_form    

 superelliptic/                 superelliptic_drw_cech         superelliptic_function         superelliptic_witt            

 superelliptic_cech             superelliptic_drw_form         superelliptic_regular_drw_form                               



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 superelliptic                 





 <unknown> [?7h[?12l[?25h[?25l[?7l_drw/

 superelliptic                  superelliptic_drw/            [?7h[?12l[?25h[?25l[?7lform

 superelliptic_drw/             superelliptic_form            [?7h[?12l[?25h[?25l[?7lregular_form

 superelliptic_form             superelliptic_regular_form    [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: om = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)

[?7h[?12l[?25h[?2004l
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [30], in <cell line: 1>()
----> 1 om = superelliptic_regular_form(Integer(0)*C.x, C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.one)

File <string>:39, in __add__(self, other)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lsage: om = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(x^3 + 2*x^2 + 2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (x^3 + 2*x^2 + 2) dy
m dy x^3
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
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^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 om.int()

File <string>:44, in int(self)

File <string>:44, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 44 (1 times)]

File <string>:35, in int(self)

    [... skipping similar frames: int at line 44 (108 times), int at line 35 (108 times)]

File <string>:44, in int(self)

File <string>:35, in int(self)

File <string>:43, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:70, in __rmul__(self, constant)

File <string>:14, in __init__(self, C, g)

File <string>:223, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    408 
    409         # Make polynomial ring over all variables except var.
--> 410         S = R.base_ring()[tuple(Z)]
    411         ring = S[var]
    412         if not self:

File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
   1273         except AttributeError:
   1274             return self.list()[n]
-> 1275     return meth(n)
   1276 
   1277 #########################################################################

File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
   1173 # 2. Otherwise, try to return a polynomial ring
   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:51, in PolynomialRing(base_ring, *args, **kwds)
     45 _cache = sage.misc.weak_dict.WeakValueDictionary()
     48 # The signature for this function is too complicated to express sensibly
     49 # in any other way besides *args and **kwds (in Python 3 or Cython, we
     50 # could probably do better thanks to PEP 3102).
---> 51 def PolynomialRing(base_ring, *args, **kwds):
     52     r"""
     53     Return the globally unique univariate or multivariate polynomial
     54     ring with given properties and variable name or names.
   (...)
    551         TypeError: unable to convert 'x' to an integer
    552     """
    553     if not ring.is_Ring(base_ring):

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ly + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l^ + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l2 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l+ + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lC + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l. + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lx + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (x^3 + 2*x^2 + 2) dy
m dy x^3
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m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [35], in <cell line: 1>()
----> 1 om.int()

File <string>:44, in int(self)

File <string>:44, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 44 (1 times)]

File <string>:35, in int(self)

    [... skipping similar frames: int at line 44 (58 times), int at line 35 (58 times)]

File <string>:44, in int(self)

File <string>:35, in int(self)

File <string>:43, in int(self)

File <string>:51, in __sub__(self, other)

File <string>:216, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    113 if coerce:
    114     self.__numerator   = parent.ring()(numerator)
--> 115     self.__denominator = parent.ring()(denominator)
    116 else:
    117     self.__numerator   = numerator

File /ext/sage/9.7/src/sage/rings/fraction_field.py:506, in FractionField_generic.ring(self)
    503     s = 'FieldOfFractions(%s)' % self.ring()._magma_init_(magma)
    504     return magma._with_names(s, self.variable_names())
--> 506 def ring(self):
    507     """
    508     Return the ring that this is the fraction field of.
    509 
   (...)
    516         Multivariate Polynomial Ring in x, y over Rational Field
    517     """
    518     return self._R

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.form().int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 om.form().int()

File <string>:199, in int(self)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
   3992 cdef Py_ssize_t n
   3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
   3996 return S(p)

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lFxy,Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lom =superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lFxy,Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lform() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lsage: om.form().int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 om.form().int()

File <string>:199, in int(self)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
   3992 cdef Py_ssize_t n
   3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
   3996 return S(p)

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om == g.diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 om == g.diffn()

File <string>:12, in __eq__(self, other)

AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom == g.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. = g.difn()[?7h[?12l[?25h[?25l[?7lf = g.difn()[?7h[?12l[?25h[?25l[?7lo = g.difn()[?7h[?12l[?25h[?25l[?7lfor = g.difn()[?7h[?12l[?25h[?25l[?7lform = g.difn()[?7h[?12l[?25h[?25l[?7l( = g.difn()[?7h[?12l[?25h[?25l[?7l() = g.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om.form() == g.diffn()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form() == g.diffn()[?7h[?12l[?25h[?25l[?7l == g.diffn()[?7h[?12l[?25h[?25l[?7l.form().int[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form() == g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega8_lift0.omega8 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l == g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.form() == g.diffn()[?7h[?12l[?25h[?25l[?7lregular_form().it()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lform() == om[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((2*x^8 + 2)/(x^4 + x^2 + 1))*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form().form() == om[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lform().form() == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^16
int(self) (2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^12
int(self) (2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^10
int(self) (2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx 1
int(self) (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dy x^6
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
^Cint(self) (2*x^4 + 2*x^2 + 2) dy
---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 om.regular_form().int()

File <string>:35, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 35 (3 times)]

File <string>:44, in int(self)

File <string>:44, in int(self)

    [... skipping similar frames: int at line 35 (70 times), int at line 44 (69 times)]

File <string>:44, in int(self)

File <string>:35, in int(self)

File <string>:21, in int(self)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(2*x^4 + 2*x^2 + 2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldy[?7h[?12l[?25h[?25l[?7lCdy[?7h[?12l[?25h[?25l[?7l.dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l*)*C.y.difn()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn()[?7h[?12l[?25h[?25l[?7lo)*C.y.difn()[?7h[?12l[?25h[?25l[?7ln)*C.y.difn()[?7h[?12l[?25h[?25l[?7le)*C.y.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l.x^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^4 + 2*C.x^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l.x^4 + 2*C.x^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.form() == om[?7h[?12l[?25h[?25l[?7lis_regular()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.int()

[?7h[?12l[?25h[?2004l[?7h(x^2 + 2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr_form()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.regular_form().int()

[?7h[?12l[?25h[?2004lint(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 om1.regular_form().int()

File <string>:44, in int(self)

File <string>:35, in int(self)

File <string>:44, in int(self)

File <string>:35, in int(self)

    [... skipping similar frames: int at line 44 (68 times), int at line 35 (67 times)]

File <string>:35, in int(self)

File <string>:44, in int(self)

File <string>:24, in int(self)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:70, in __rmul__(self, constant)

File <string>:14, in __init__(self, C, g)

File <string>:214, in reduction(C, g)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.regular_form().int()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.regular_form().int()[?7h[?12l[?25h[?25l[?7l1 = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.regular_form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lregular_form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h((2*x^8 + 2)/(x^4 + x^2 + 1))*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.regular_form().int()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l*([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1.int()

[?7h[?12l[?25h[?2004l[?7h(x^2 + 2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h((-x^4 - x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h((-x^4 - x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1.int().diffn() == om1

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int().diffn() == om1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.int().diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^4 - x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C.polynomial

[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.polynomial)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (C.polynomial)^2

[?7h[?12l[?25h[?2004l[?7hx^6 + x^4 + x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7luC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7ltC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7loC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lmC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l(C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Input In [59] in <cell line: 1>
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:3 in <module>

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:203
    "If omega is regular, return form eta such that Cartier(eta) = omega"
    ^
IndentationError: expected an indented block after function definition on line 202

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()

File <string>:78, in coordinates(self, basis)

File <string>:207, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx None
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()

File <string>:78, in coordinates(self, basis)

File <string>:208, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
fct ((x^2 + 2*x + 1)/(x + 2))*y
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((x + 1)/(x*y - y)) dx, 0, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
coordinates of form self ((x + 1)/(x*y - y)) dx
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [65], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()

File <string>:92, in coordinates(self, basis)

File <string>:56, in coordinates(self)

File <string>:94, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(0, 9):[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((x^2 + 2*x + 1)/(x + 2))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + 2*x + 1)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l.x^2 + 2*x + 1)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx + 1)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l.x + 1)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/(x + 2)*y[?7h[?12l[?25h[?25l[?7lC)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l.)/(x + 2)*y[?7h[?12l[?25h[?25l[?7lo)/(x + 2)*y[?7h[?12l[?25h[?25l[?7ln)/(x + 2)*y[?7h[?12l[?25h[?25l[?7le)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx + 2)*y[?7h[?12l[?25h[?25l[?7l.x + 2)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*))*y[?7h[?12l[?25h[?25l[?7lC))*y[?7h[?12l[?25h[?25l[?7lo))*y[?7h[?12l[?25h[?25l[?7ln))*y[?7h[?12l[?25h[?25l[?7l))*y[?7h[?12l[?25h[?25l[?7l))*y[?7h[?12l[?25h[?25l[?7l))*y[?7h[?12l[?25h[?25l[?7lC))*y[?7h[?12l[?25h[?25l[?7l.))*y[?7h[?12l[?25h[?25l[?7lo))*y[?7h[?12l[?25h[?25l[?7ln))*y[?7h[?12l[?25h[?25l[?7le))*y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^4 - x^3 - x^2 - x + 1)/(x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautomC.crystalline_cohomlogy_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lff = (C.x^2 + 2*C.x + C.ne)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmf.difn()[?7h[?12l[?25h[?25l[?7lf.difn()[?7h[?12l[?25h[?25l[?7lof.difn()[?7h[?12l[?25h[?25l[?7lmf.difn()[?7h[?12l[?25h[?25l[?7l f.difn()[?7h[?12l[?25h[?25l[?7l=f.difn()[?7h[?12l[?25h[?25l[?7l f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ff.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = ff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsage: om.is_regular_on_U

 om.is_regular_on_U0    

 om.is_regular_on_Uinfty





 [?7h[?12l[?25h[?25l[?7l0

 om.is_regular_on_U0    



 <unknown> [?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l = ff.diffn()[?7h[?12l[?25h[?25l[?7lff.din()[?7h[?12l[?25h[?25l[?7l = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lautomC.crystalline_cohomlogy_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
  """
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
  """
---------------------------------------------------------------------------
RecursionError                            Traceback (most recent call last)
Input In [71], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()

File <string>:95, in coordinates(self, basis)

File <string>:70, in coordinates(self)

File <string>:70, in coordinates(self)

    [... skipping similar frames: coordinates at line 70 (2941 times)]

File <string>:70, in coordinates(self)

File <string>:50, in coordinates(self)

File <string>:98, in de_rham_basis(self)

File <string>:91, in basis_de_rham_degrees(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File <string>:259, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1007 try:
   1008     # now try calling the base ring's __call__ methods
-> 1009     element = self.base_ring()(element)
   1010     _p = p_NSet(sa2si(element,_ring), _ring)
   1011     return new_MP(self,_p)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    378 else:
    379     try:
--> 380         z = integer_ring.Z(value)
    381     except (TypeError, ValueError):
    382         from sage.structure.element import Expression

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    829     return R(self.__numerator)
    830 else:
--> 831     self.reduce()
    832     num = R(self.__numerator)
    833     inv_den = R(self.__denominator).inverse_of_unit()

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
   1237 if self._is_reduced:
   1238     return
-> 1239 super(self.__class__, self).reduce()
   1240 self.normalize_leading_coefficients()
   1241 

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    162     return codomain.coerce(nnum/nden)
    163 
--> 164 cpdef reduce(self):
    165     """
    166     Reduce this fraction.

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    195     return
    196 try:
--> 197     g = self.__numerator.gcd(self.__denominator)
    198     if not g.is_unit():
    199         self.__numerator //= g

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4911         raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
   4912     else:
-> 4913         return doit(self, other)
   4914 
   4915 @coerce_binop

File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
    944 f1 = Num(f.numerator())
    945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4905 if tgt.ngens() > 1 and tgt._has_singular:
   4906     g = flatten(self).gcd(flatten(other))
-> 4907     return flatten.section()(g)
   4908 try:
   4909     doit = self._parent._base._gcd_univariate_polynomial

File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
    767 if P is D: # we certainly want to call _call_/with_args
    768     if not args and not kwds:
--> 769         return self._call_(x)
    770     return self._call_with_args(x, args, kwds)
    771 # Is there coercion?

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:397, in UnflatteningMorphism._call_(self, p)
    395     newpol[l - 1] = {}
    396 if (i == len(expo) - 1 or expo[i + 1][idx:] != cur_exp[idx:]):
--> 397     newpol[l] = R(newpol[l], check=False)
    398 else:
    399     break

File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__()
    897         return mor._call_(x)
    898     else:
--> 899         return mor._call_with_args(x, args, kwds)
    900 
    901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {}))

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:180, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
    178     print(type(C), C)
    179     print(type(C._element_constructor), C._element_constructor)
--> 180 raise
    181 
    182 

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
    168         return C._element_constructor(x)
    169     else:
--> 170         return C._element_constructor(x, **kwds)
    171 else:
    172     if len(kwds) == 0:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    467 elif isinstance(x, sage.rings.power_series_ring_element.PowerSeries):
    468     x = x.truncate()
--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
    127         except AttributeError:
    128             pass
--> 129     Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
    130 
    131 cdef Polynomial_template _new(self):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:158, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
    156 for deg, coef in x.iteritems():
    157     celement_pow(monomial, gen, deg, NULL, (<Polynomial_template>self)._cparent)
--> 158     celement_mul(monomial, &(<Polynomial_template>self.__class__(parent, coef)).x, monomial, (<Polynomial_template>self)._cparent)
    159     celement_add(&self.x, &self.x, monomial, (<Polynomial_template>self)._cparent)
    160 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
    127         except AttributeError:
    128             pass
--> 129     Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
    130 
    131 cdef Polynomial_template _new(self):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:107, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
    105 cdef Py_ssize_t deg
    106 
--> 107 Polynomial.__init__(self, parent, is_gen=is_gen)
    108 
    109 (<Polynomial_template>self)._cparent = get_cparent(self._parent)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:233, in sage.rings.polynomial.polynomial_element.Polynomial.__init__()
    231     True
    232 """
--> 233 CommutativeAlgebraElement.__init__(self, parent)
    234 self._is_gen = is_gen
    235 

RecursionError: maximum recursion depth exceeded while calling a Python object
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = ((C.x^2 + C.x)*C.y^2*C.y.diffn()).verschiebung() + ((2*C.x^7 + C.x^6 + C.x^5 + C.x^4 + 2*C.x^3+C.x^2+2*C.x)*C.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomolog_basis[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lBcrys[1]) - Bcrys[0] - Bcry[1][?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [74], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)

File <string>:100, in coordinates(self, basis)

File <string>:70, in coordinates(self)

File <string>:70, in coordinates(self)

    [... skipping similar frames: coordinates at line 70 (940 times)]

File <string>:70, in coordinates(self)

File <string>:60, in coordinates(self)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File <string>:143, in expansion_at_infty(self, place, prec)

File <string>:135, in expansion_at_infty(self, place, prec)

File <string>:18, in naive_hensel(fct, F, start, prec)

File /ext/sage/9.7/src/sage/rings/big_oh.py:141, in O(*x, **kwds)
    138     return x.parent().completion(x.parent().gen())(0, x.degree(), **kwds)
    140 elif isinstance(x, laurent_series_ring_element.LaurentSeries):
--> 141     return laurent_series_ring_element.LaurentSeries(x.parent(), 0).\
    142         add_bigoh(x.valuation(), **kwds)
    144 elif isinstance(x, PuiseuxSeries):
    145     return x.add_bigoh(x.valuation(), **kwds)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:148, in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()
    146     f = parent._power_series_ring(f)
    147 elif not isinstance(f, PowerSeries):
--> 148     f = parent._power_series_ring(f)
    149 ## now this is a power series, over a different ring ...
    150 ## requires that power series rings with same vars over the

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/power_series_ring.py:823, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check)
    821         else:
    822             raise TypeError("Can only convert series into ring with same variable name.")
--> 823 return self.element_class(self, f, prec, check=check)

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
     42     ValueError: series has negative valuation
     43 """
---> 44 R = parent._poly_ring()
     45 if isinstance(f, Element):
     46     if (<Element>f)._parent is R:

File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
    958         pass
    959     return False
--> 961 def _poly_ring(self):
    962     """
    963     Return the underlying polynomial ring used to represent elements of
    964     this power series ring.
   (...)
    970         Univariate Polynomial Ring in t over Integer Ring
    971     """
    972     return self.__poly_ring

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7lg((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l ((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l=((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l ((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx + 1)*y[?7h[?12l[?25h[?25l[?7l.x + 1)*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))*y[?7h[?12l[?25h[?25l[?7lC))*y[?7h[?12l[?25h[?25l[?7l.))*y[?7h[?12l[?25h[?25l[?7lo))*y[?7h[?12l[?25h[?25l[?7ln))*y[?7h[?12l[?25h[?25l[?7le))*y[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lroot[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.pth_root()

[?7h[?12l[?25h[?2004l[?7h((2*x^2 + x + 2)/(x + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^12 + x^10 + x^6 - x^4)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7lm((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7lm((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l1((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l ((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l=((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l ((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = (-C.x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy) C.dx[?7h[?12l[?25h[?25l[?7l.y) C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = ((-C.x^12 + C.x^10 + C.x^6 - C.x^4)/C.y)* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^12 + C.x^10 + C.x^6 - C.x^4)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2-om[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l== om[?7h[?12l[?25h[?25l[?7l (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + x^2 + x)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + x^2 + x)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + x)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + x)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.y)* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRcartier(om1) -[?7h[?12l[?25h[?25l[?7l cartier(om1) -[?7h[?12l[?25h[?25l[?7l=cartier(om1) -[?7h[?12l[?25h[?25l[?7l cartier(om1) -[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R = om1.cartier() - om2.cartier()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR = om1.cartier() - om2.cartier()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R == gg.pth_root()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [80], in <cell line: 1>()
----> 1 R == gg.pth_root()

File <string>:12, in __eq__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'reduce'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR == gg.pth_root()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R == gg.pth_root().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lth[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1.cartier(), gg.pth_root())

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [83], in <cell line: 1>()
----> 1 xi.coordinates()

File <string>:70, in coordinates(self)

File <string>:70, in coordinates(self)

    [... skipping similar frames: coordinates at line 70 (91 times)]

File <string>:70, in coordinates(self)

File <string>:66, in coordinates(self)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File <string>:142, in expansion_at_infty(self, place, prec)

File <string>:137, in expansion_at_infty(self, place, prec)

File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
   1512 cdef int cl = classify_elements(left, right)
   1513 if HAVE_SAME_PARENT(cl):
-> 1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
   1516     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
    911 cdef LaurentSeries right = <LaurentSeries>right_r
    912 return type(self)(self._parent,
--> 913                   self.__u * right.__u,
    914                   self.__n + right.__n)
    915 

File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
   1512 cdef int cl = classify_elements(left, right)
   1513 if HAVE_SAME_PARENT(cl):
-> 1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
   1516     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
    538 """
    539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
    541                         self.__f * (<PowerSeries_poly>right_r).__f,
    542                         prec=prec,

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
     42     ValueError: series has negative valuation
     43 """
---> 44 R = parent._poly_ring()
     45 if isinstance(f, Element):
     46     if (<Element>f)._parent is R:

File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
    958         pass
    959     return False
--> 961 def _poly_ring(self):
    962     """
    963     Return the underlying polynomial ring used to represent elements of
    964     this power series ring.
   (...)
    970         Univariate Polynomial Ring in t over Integer Ring
    971     """
    972     return self.__poly_ring

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: xi1

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 xi1

NameError: name 'xi1' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi1[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7loordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [87], in <cell line: 1>()
----> 1 xi.coordinates()

File <string>:50, in coordinates(self)

File <string>:98, in de_rham_basis(self)

File <string>:76, in basis_de_rham_degrees(self)

File <string>:60, in holomorphic_differentials_basis(self)

File <string>:52, in basis_holomorphic_differentials_degree(self)

File <string>:7, in __init__(self, C, g)

File <string>:259, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))
    710 try:
--> 711     return self._element_class(self, x, y, coerce=coerce)
    712 except TypeError:
    713     if parent(x) is parent(x0):

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    113 if coerce:
    114     self.__numerator   = parent.ring()(numerator)
--> 115     self.__denominator = parent.ring()(denominator)
    116 else:
    117     self.__numerator   = numerator

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
    336 """
    337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
--> 338     return repr(self.numer())
    339 else:
    340     numer_s = repr(self.numer())

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7lR =gg.pth_roo().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l om1cartier() - om2.cartier()[?7h[?12l[?25h[?25l[?7lom2= ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l112 + C.x^10+ C.x^6 - C.x^4)/C.y) C.dx[?7h[?12l[?25h[?25l[?7lgg.pth_root()[?7h[?12l[?25h[?25l[?7l = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lautomB[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lfomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [90], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)

File <string>:99, in coordinates(self, basis)

File <string>:85, in div_by_p(self)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx

[?7h[?12l[?25h[?2004l  Input In [91]
    ((-x**Integer(3) + x**Integer(2) + x)/(x**Integer(2)*y + x*y + y)) dx
                                                                       ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7lsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: om2

[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: om2.expansion

 om2.expansion         

 om2.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 om2.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 om2.expansion         

 om2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 +x)/(*y+ *y + y)) dx[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 +x)/(*y+ *y + y)) dx[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
(1, 1)
aux 0 ( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [97], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)

File <string>:100, in coordinates(self, basis)

File <string>:86, in div_by_p(self)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/categories/rings.py:1129, in Rings.ParentMethods.__getitem__(self, arg)
   1128 try:
-> 1129     minpolys = [a.minpoly() for a in elts]
   1130 except (AttributeError, NotImplementedError, ValueError, TypeError):

File /ext/sage/9.7/src/sage/categories/rings.py:1129, in <listcomp>(.0)
   1128 try:
-> 1129     minpolys = [a.minpoly() for a in elts]
   1130 except (AttributeError, NotImplementedError, ValueError, TypeError):

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    493 """
--> 494 return self.getattr_from_category(name)
    495 

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    506     cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
    508 

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr

AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'minpoly'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Input In [99], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)

File <string>:53, in crystalline_cohomology_basis(self, prec)

File <string>:24, in de_rham_witt_lift(cech_class, prec)

File <string>:6, in de_rham_witt_lift_form0(omega)

File <string>:99, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:31, in __add__(self, other)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:70, in __rmul__(self, constant)

File <string>:14, in __init__(self, C, g)

File <string>:223, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    409 # Make polynomial ring over all variables except var.
    410 S = R.base_ring()[tuple(Z)]
--> 411 ring = S[var]
    412 if not self:
    413     return ring(0)

File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
   1273         except AttributeError:
   1274             return self.list()[n]
-> 1275     return meth(n)
   1276 
   1277 #########################################################################

File /ext/sage/9.7/src/sage/categories/rings.py:1129, in Rings.ParentMethods.__getitem__(self, arg)
   1126 elts = normalize_arg(arg)
   1128 try:
-> 1129     minpolys = [a.minpoly() for a in elts]
   1130 except (AttributeError, NotImplementedError, ValueError, TypeError):
   1131     minpolys = None

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7luautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lxautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l autom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l=autom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l autom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx1[?7h[?12l[?25h[?25l[?7lsage: aux

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loaux.omega8[?7h[?12l[?25h[?25l[?7lmaux.omega8[?7h[?12l[?25h[?25l[?7l aux.omega8[?7h[?12l[?25h[?25l[?7l=aux.omega8[?7h[?12l[?25h[?25l[?7l aux.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = aux.omega8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = aux.omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h[((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = aux.omega8[?7h[?12l[?25h[?25l[?7l-u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7lt.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7li.difn()[?7h[?12l[?25h[?25l[?7lc.difn()[?7h[?12l[?25h[?25l[?7lh.difn()[?7h[?12l[?25h[?25l[?7lm.difn()[?7h[?12l[?25h[?25l[?7lu.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7lr.difn()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l_.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om - aux.f.t.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[((x^2 + x + 2)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^8 - x^6 + x^4 - x^3 + x - 1)/(x^7*y - x^6*y - x^5*y - x^4*y - x^3*y - x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lmom - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l1om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = om + aux.f.t.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om + aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.int().diffn()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lform() == om[?7h[?12l[?25h[?25l[?7lrobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lni[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.frobenius()

[?7h[?12l[?25h[?2004l[?7h(1/(x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lxpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om1.frobenius().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^4 + 2*t^6 + t^8 + O(t^14)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lar[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.omega.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lsage: om1.omega.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lais_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lris_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7ltis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7leis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lris_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l(is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l()is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1.omega.cartier().is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.cartier().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: om2 = om1.omega

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2 = second_patch(om1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = second_patch(om1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = second_patch(om1)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom1.omeg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega[?7h[?12l[?25h[?25l[?7lsage: om2 = om1.omega

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.omega[?7h[?12l[?25h[?25l[?7lsecond_ptch(om1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = second_patch(om2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = second_patch(om2)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.expansion__infty()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2.cartier()

[?7h[?12l[?25h[?2004l[?7h((x + 1)/(x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1omega.cartier().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7l2.cartier()[?7h[?12l[?25h[?25l[?7l = second_patch(om2)[?7h[?12l[?25h[?25l[?7lom1.omeg[?7h[?12l[?25h[?25l[?7lsecond_ptch(om1)[?7h[?12l[?25h[?25l[?7lom1.omeg[?7h[?12l[?25h[?25l[?7l1.omegacartier().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lfrobenus().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = om + aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l - aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = aux.omega8[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(bsi = B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lx = autom(B[1]).coordinte(basis = B)[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(bsi = B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [119], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)

AttributeError: 'NoneType' object has no attribute 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
aux 0 ( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [120], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)

File <string>:100, in coordinates(self, basis)

File <string>:86, in div_by_p(self)

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7lm((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l2((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l ((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l ((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l=((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l ((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^3 + x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l/x^3 + x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7lx^3 + x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x^3 + x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x*y + y)* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + y)* dx[?7h[?12l[?25h[?25l[?7l.y + y)* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy)* dx[?7h[?12l[?25h[?25l[?7l.y)* dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC dx[?7h[?12l[?25h[?25l[?7l. dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpip install -U sage[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lc()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [124], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)

File <string>:101, in coordinates(self, basis)

File <string>:70, in coordinates(self)

File <string>:70, in coordinates(self)

    [... skipping similar frames: coordinates at line 70 (234 times)]

File <string>:70, in coordinates(self)

File <string>:60, in coordinates(self)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File <string>:143, in expansion_at_infty(self, place, prec)

File <string>:135, in expansion_at_infty(self, place, prec)

File <string>:18, in naive_hensel(fct, F, start, prec)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:895, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    893     result = pol.get_unsafe(d)
    894     for i in xrange(d - 1, -1, -1):
--> 895         result = result * a + pol.get_unsafe(i)
    896     return result
    897 pol._compiled = CompiledPolynomialFunction(pol.list())

File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
   1512 cdef int cl = classify_elements(left, right)
   1513 if HAVE_SAME_PARENT(cl):
-> 1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
   1516     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
    911 cdef LaurentSeries right = <LaurentSeries>right_r
    912 return type(self)(self._parent,
--> 913                   self.__u * right.__u,
    914                   self.__n + right.__n)
    915 

File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
   1512 cdef int cl = classify_elements(left, right)
   1513 if HAVE_SAME_PARENT(cl):
-> 1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
   1516     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
    538 """
    539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
    541                         self.__f * (<PowerSeries_poly>right_r).__f,
    542                         prec=prec,

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
     42     ValueError: series has negative valuation
     43 """
---> 44 R = parent._poly_ring()
     45 if isinstance(f, Element):
     46     if (<Element>f)._parent is R:

File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
    958         pass
    959     return False
--> 961 def _poly_ring(self):
    962     """
    963     Return the underlying polynomial ring used to represent elements of
    964     this power series ring.
   (...)
    970         Univariate Polynomial Ring in t over Integer Ring
    971     """
    972     return self.__poly_ring

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [125], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)

File <string>:100, in coordinates(self, basis)

File <string>:86, in div_by_p(self)

File <string>:26, in __sub__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
^C---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:609, in PolynomialRing(base_ring, *args, **kwds)
    608 try:
--> 609     k = Integer(arg)
    610 except TypeError:
    611     # Interpret arg as names

File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
    716 
--> 717                 raise TypeError("unable to coerce %s to an integer" % type(x))
    718 

TypeError: unable to coerce <class 'tuple'> to an integer

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Input In [126], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)

File <string>:102, in coordinates(self, basis)

File <string>:70, in coordinates(self)

File <string>:70, in coordinates(self)

    [... skipping similar frames: coordinates at line 70 (133 times)]

File <string>:70, in coordinates(self)

File <string>:50, in coordinates(self)

File <string>:98, in de_rham_basis(self)

File <string>:91, in basis_de_rham_degrees(self)

File <string>:7, in __init__(self, C, g)

File <string>:259, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
    704 x0, y0 = x, y
    705 try:
--> 706     x, y = resolve_fractions(x0, y0)
    707 except (AttributeError, TypeError):
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))

File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
    686 yd = y.denominator()
    687 try:
--> 688     return (xn * yd, yn * xd)
    689 except (AttributeError, TypeError, ValueError):
    690     pass

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1198 # Now coerce to a common parent and do the operation there
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:
   1202     self._record_exception()

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1309 x_map, y_map = coercions
   1310 if x_map is not None:
-> 1311     x_elt = (<Map>x_map)._call_(x)
   1312 else:
   1313     x_elt = x

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    408 
    409         # Make polynomial ring over all variables except var.
--> 410         S = R.base_ring()[tuple(Z)]
    411         ring = S[var]
    412         if not self:

File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
   1273         except AttributeError:
   1274             return self.list()[n]
-> 1275     return meth(n)
   1276 
   1277 #########################################################################

File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
   1173 # 2. Otherwise, try to return a polynomial ring
   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:609, in PolynomialRing(base_ring, *args, **kwds)
    607 for arg in args:
    608     try:
--> 609         k = Integer(arg)
    610     except TypeError:
    611         # Interpret arg as names
    612         if names is not None:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((x + 1)/(x*y - y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l/dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx*y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x*y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx + 1)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x + 1)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7lC)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7lo)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7ln)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7le)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = ((C.x + C.one)/(C.x*C.y - C.y))* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((C.x + C.one)/(C.x*C.y - C.y))* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = om + aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((-x^3 + x)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)*C.dx[?7h[?12l[?25h[?25l[?7l.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l/dx[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + C.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + C.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = ((-C.x^3 + C.x)/C.y)* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: om1 - f1.diffn() == om2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [131], in <cell line: 1>()
----> 1 om1 - f1.diffn() == om2

AttributeError: 'superelliptic_form' object has no attribute 'diffn'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((-C.x^3 + C.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((2*x^2 + x + 2)/(x + 2))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx + 2)*C.y[?7h[?12l[?25h[?25l[?7l.x + 2)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*))*C.y[?7h[?12l[?25h[?25l[?7lC))*C.y[?7h[?12l[?25h[?25l[?7l.))*C.y[?7h[?12l[?25h[?25l[?7lo))*C.y[?7h[?12l[?25h[?25l[?7ln))*C.y[?7h[?12l[?25h[?25l[?7le))*C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lo)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7ln)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l>x + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.x + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + C.x + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.x^2 + C.x + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lsage: om1 - f1.diffn() == om2

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn() == om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: xi.omega8 == omega2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [135], in <cell line: 1>()
----> 1 xi.omega8 == omega2

NameError: name 'omega2' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8 == omega2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.omega8 == om2

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8 == om2[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [137], in <cell line: 1>()
----> 1 xi.coordinates()

File <string>:70, in coordinates(self)

File <string>:70, in coordinates(self)

    [... skipping similar frames: coordinates at line 70 (516 times)]

File <string>:70, in coordinates(self)

File <string>:66, in coordinates(self)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File <string>:143, in expansion_at_infty(self, place, prec)

File <string>:135, in expansion_at_infty(self, place, prec)

File <string>:18, in naive_hensel(fct, F, start, prec)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:881, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    879 d = pol.degree()
    880 
--> 881 if d <= 0 or (isinstance(a, Element) and R.is_exact() and a.is_zero()):
    882     return cst # with the right parent thanks to the above coercion
    883 elif pol._parent is R and a.is_gen():

File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:715, in LaurentSeriesRing.is_exact(self)
    703     """
    704     Get the precision to which exact elements are truncated when
    705     necessary (most frequently when inverting).
   (...)
    711         5
    712     """
    713     return self._power_series_ring.default_prec()
--> 715 def is_exact(self):
    716     """
    717     Laurent series rings are inexact.
    718 
   (...)
    723         False
    724     """
    725     return False

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1

[?7h[?12l[?25h[?2004l[?7h((2*x^2 + x + 2)/(x + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lf1.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7lomega8 == om2[?7h[?12l[?25h[?25l[?7lega2[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn() == om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lf1.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7lomega8 == om2[?7h[?12l[?25h[?25l[?7lega2[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn() == om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lf1 = ((-C.x^3 + C.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lom1 = (-C.x^3 + C.x)/C.y)*[?7h[?12l[?25h[?25l[?7lsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7l= superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004lcoordinates of (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
^R
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [146], in <cell line: 1>()
----> 1 xi.coordinates()

File <string>:72, in coordinates(self)

File <string>:72, in coordinates(self)

    [... skipping similar frames: coordinates at line 72 (49 times)]

File <string>:72, in coordinates(self)

File <string>:67, in coordinates(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:23, in __rmul__(self, constant)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File <string>:245, in reduction_form(C, g)

File <string>:223, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    408 
    409         # Make polynomial ring over all variables except var.
--> 410         S = R.base_ring()[tuple(Z)]
    411         ring = S[var]
    412         if not self:

File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
   1273         except AttributeError:
   1274             return self.list()[n]
-> 1275     return meth(n)
   1276 
   1277 #########################################################################

File /ext/sage/9.7/src/sage/categories/rings.py:1103, in Rings.ParentMethods.__getitem__(self, arg)
   1099         return (arg,)
   1101 # 1. If arg is a list, try to return a power series ring.
-> 1103 if isinstance(arg, list):
   1104     if not arg:
   1105         raise TypeError("power series rings must have at least one variable")

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lf1 = (2*2 + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lf1 = (2*2 + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004lcoordinates of (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coordinates of (0 dx, 0, 0 dx)
[?7h(0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lutom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coord_aux_divided_by_p (0, 1)
[?7h[1, 4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

....: muller())[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

....: muller())

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

....: muller())[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.omega0.regular_fom()

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.coordinates(basis = B)

[?7h[?12l[?25h[?2004l(0, 1)
omega, omega_regular 0 dx (0) dy
omega, omega_regular 0 dx (0) dy
aux (0, V(((x^16 + x^10)/(x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2))*y), V(((-x^8 + x^6 - 1)/y) dx))
aux_divided_by_p (0 dx, ((x^5 + x^3)/(x^4 + x^2 + 1))*y, ((-x^3)/y) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, ((x^5 + x^3)/(x^4 + x^2 + 1))*y, ((-x^3)/y) dx)
coordinates of form self ((-x^3)/y) dx
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [155], in <cell line: 1>()
----> 1 eta2.coordinates(basis = B)

File <string>:102, in coordinates(self, basis)

File <string>:73, in coordinates(self)

File <string>:59, in coordinates(self)

File <string>:94, in coordinates(self, basis)

File <string>:16, in linear_representation_polynomials(polynomial, list_of_polynomials)

File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:903, in sage.matrix.matrix2.Matrix.solve_right()
    901 
    902         if not self.is_square():
--> 903             X = self._solve_right_general(C, check=check)
    904         else:
    905             try:

File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:1026, in sage.matrix.matrix2.Matrix._solve_right_general()
   1024     # Have to check that we actually solved the equation.
   1025     if self*X != B:
-> 1026         raise ValueError("matrix equation has no solutions")
   1027 return X
   1028 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^8 + x^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.y)* C.dx[?7h[?12l[?25h[?25l[?7l/y)* C.dx[?7h[?12l[?25h[?25l[?7ly)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC1)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.1)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lo)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7ln)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7le)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l/x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lx^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l=(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lsage: omm = (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx

[?7h[?12l[?25h[?2004l  Input In [156]
    omm = (-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y)* C.dx
                                                          ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omm = (-C.x^8 + C.x^6 - C.one)/C.y* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = (-C.x^8 + C.x^6 - C.one)/C.y* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omm.expansion

 omm.expansion         

 omm.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 omm.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 omm.expansion         

 omm.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omm.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-16 + 2*t^-8 + O(t^-6)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lomm.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omm.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-6 + t^-2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7leta2.coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8

[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7lm((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7lm((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l ((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l=((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l ((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l.x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l.x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1)/y) dx)[?7h[?12l[?25h[?25l[?7l.1)/y) dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l.)/y) dx)[?7h[?12l[?25h[?25l[?7lo)/y) dx)[?7h[?12l[?25h[?25l[?7ln)/y) dx)[?7h[?12l[?25h[?25l[?7le)/y) dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy) dx)[?7h[?12l[?25h[?25l[?7l.y) dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCdx)[?7h[?12l[?25h[?25l[?7l.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx)

[?7h[?12l[?25h[?2004l  Input In [162]
    omm = ((-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y) C.dx)
                                                                 ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx

[?7h[?12l[?25h[?2004l  Input In [163]
    omm = ((-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y) C.dx
                                                             ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y)* C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = ((-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_ifty()[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: omm.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-6 + t^-2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8

[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
sage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())


[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega8 == om1[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta1.coordinates()

[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
(1, 0)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular 0 dx (0) dy
omega, omega_regular 0 dx (0) dy
aux (0, [0], V(((-x^3)/y) dx))
aux_divided_by_p (0 dx, 0, 0 dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, 0, 0 dx)
coord_aux_divided_by_p (0, 0)
[?7h[1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2omega8[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2omega8[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

....: muller())[?7h[?12l[?25h[?25l[?7l-ax

 [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: eta2 - B[1]

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^8 + x^6 - 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]), V((2*x^4 + 2*x^2 + 2)*y), V(((-x^8 + x^6 - 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7l1.coordinates()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
2.omega8[?7h[?12l[?25h[?25l[?7l1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
.coordinates()[?7h[?12l[?25h[?25l[?7l2 - B[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l[0].omega0.regular_frm()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B[1].omega8

[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7l1.coordinates()[?7h[?12l[?25h[?25l[?7l2 - B[1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.coordinates()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
2.omega8[?7h[?12l[?25h[?25l[?7lomm.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((-C.x^8 + C.x^6 - C.oe)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_ifty()[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega8[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].omega8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[1].omega8.r()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega8.r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lseB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lcB[1].omega8.r()[?7h[?12l[?25h[?25l[?7loB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lnB[1].omega8.r()[?7h[?12l[?25h[?25l[?7ldB[1].omega8.r()[?7h[?12l[?25h[?25l[?7l_B[1].omega8.r()[?7h[?12l[?25h[?25l[?7lpB[1].omega8.r()[?7h[?12l[?25h[?25l[?7laB[1].omega8.r()[?7h[?12l[?25h[?25l[?7ltB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lcB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lhB[1].omega8.r()[?7h[?12l[?25h[?25l[?7l(B[1].omega8.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(B[1].omega8.r())

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.one/C.x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7lB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7lB[1].omega8.r()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.*v.difn()[?7h[?12l[?25h[?25l[?7lt*v.difn()[?7h[?12l[?25h[?25l[?7le*v.difn()[?7h[?12l[?25h[?25l[?7li*v.difn()[?7h[?12l[?25h[?25l[?7lc*v.difn()[?7h[?12l[?25h[?25l[?7lh*v.difn()[?7h[?12l[?25h[?25l[?7lm*v.difn()[?7h[?12l[?25h[?25l[?7lu*v.difn()[?7h[?12l[?25h[?25l[?7ll*v.difn()[?7h[?12l[?25h[?25l[?7ll*v.difn()[?7h[?12l[?25h[?25l[?7le*v.difn()[?7h[?12l[?25h[?25l[?7lr*v.difn()[?7h[?12l[?25h[?25l[?7l(*v.difn()[?7h[?12l[?25h[?25l[?7l()*v.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltdifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lidifn()[?7h[?12l[?25h[?25l[?7lcdifn()[?7h[?12l[?25h[?25l[?7lhdifn()[?7h[?12l[?25h[?25l[?7lmdifn()[?7h[?12l[?25h[?25l[?7ludifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lrdifn()[?7h[?12l[?25h[?25l[?7l(difn()[?7h[?12l[?25h[?25l[?7l()difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h + V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega8 + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laB[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7luB[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lxB[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=B[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l B[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux= B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux= B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: aux.h2.expansion

 aux.h2.expansion         

 aux.h2.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 aux.h2.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 aux.h2.expansion         

 aux.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.h2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7laux.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux.omega.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^6 + t^10 + O(t^16)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l- B[1][?7h[?12l[?25h[?25l[?7lsage: eta2 - B[1]

[?7h[?12l[?25h[?2004l[?7h( + V(((-x^8 + x^6 - 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]), V((2*x^4 + 2*x^2 + 2)*y), V(((-x^8 + x^6 - 1)/y) dx))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.omega.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coord_aux_divided_by_p (0, 1)
[?7h[1, 4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l = supereliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l(), 3)[?7h[?12l[?25h[?25l[?7l()x, 3)[?7h[?12l[?25h[?25l[?7l^, 3)[?7h[?12l[?25h[?25l[?7l3, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l(), 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l(), 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx), 3)[?7h[?12l[?25h[?25l[?7l^), 3)[?7h[?12l[?25h[?25l[?7l3), 3)[?7h[?12l[?25h[?25l[?7l ), 3)[?7h[?12l[?25h[?25l[?7l-), 3)[?7h[?12l[?25h[?25l[?7l ), 3)[?7h[?12l[?25h[?25l[?7lx), 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^, 3)[?7h[?12l[?25h[?25l[?7l3, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l+, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l1, 3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7lx, 3)[?7h[?12l[?25h[?25l[?7l^, 3)[?7h[?12l[?25h[?25l[?7l3, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l-, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7lx, 3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 3)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 3)[?7h[?12l[?25h[?25l[?7l.polynomia[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(; autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [182], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis()

File <string>:52, in crystalline_cohomology_basis(self, prec)

File <string>:98, in de_rham_basis(self)

File <string>:80, in basis_de_rham_degrees(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:94, in diffn(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
   1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
-> 1739     return coercion_model.bin_op(left, right, truediv)
   1740 
   1741 try:

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:727, in sage.rings.fraction_field_element.FractionFieldElement._div_()
    725 
    726         if snum.is_zero():
--> 727             raise ZeroDivisionError("fraction field element division by zero")
    728 
    729         rightinv = self.__class__(self._parent, sden, snum,

ZeroDivisionError: fraction field element division by zero
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 3)[?7h[?12l[?25h[?25l[?7l.polynomia[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [185], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis()

File <string>:53, in crystalline_cohomology_basis(self, prec)

File <string>:31, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [186], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100))

File <string>:53, in crystalline_cohomology_basis(self, prec)

File <string>:31, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lderham_basis()[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((x/y) dx, 0, (x/y) dx),
 ((x^2/y) dx, 0, (x^2/y) dx),
 ((x^3/y) dx, 0, (x^3/y) dx),
 ((x^7/y) dx, 2/x*y, ((-1)/(x*y)) dx),
 (((-x^6)/y) dx, 2/x^2*y, 0 dx),
 (0 dx, 2/x^3*y, (1/(x^3*y)) dx),
 ((x^4/y) dx, 2/x^4*y, ((-1)/(x^4*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.de_rham_basis([?7h[?12l[?25h[?25l[?7lB = C.crystlline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lcrystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [190], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis()

File <string>:53, in crystalline_cohomology_basis(self, prec)

File <string>:31, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lvc)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 200)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [191], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(200))

File <string>:53, in crystalline_cohomology_basis(self, prec)

File <string>:34, in de_rham_witt_lift(cech_class, prec)

File <string>:35, in decomposition_omega0_omega8(omega, prec)

File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
    583     return expression.sum(*args, **kwds)
    584 elif max(len(args),len(kwds)) <= 1:
--> 585     return sum(expression, *args, **kwds)
    586 else:
    587     from sage.symbolic.ring import SR

File <string>:35, in <genexpr>(.0)

File <string>:156, in residue(self, place, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 200)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[([(1/(x^9 + 2*x))*y] d[x] + V(((-x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]), V(x*y), [(1/(x^9 + 2*x))*y] d[x] + V(((-x)/(x^8*y - y)) dx) + dV([(x/(x^8 + 2))*y])),
 ([(1/(x^8 + 2))*y] d[x] + V(((-x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]), V(((x^8 + 1)/x^4)*y), [(1/(x^8 + 2))*y] d[x] + V(((-x^4)/(x^8*y - y)) dx) + dV([(1/(x^12 + 2*x^4))*y])),
 ([(x/(x^8 + 2))*y] d[x] + V(((-x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]), V(((x^8 + 1)/x)*y), [(x/(x^8 + 2))*y] d[x] + V(((-x^7)/(x^8*y - y)) dx) + dV([(1/(x^9 + 2*x))*y])),
 ([(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]), V((x^10 + x^2)*y), [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(x^2/(x^8 + 2))*y])),
 ([(x^6/(x^8 + 2))*y] d[x] + V(((x^14 + x^6)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]), [2/x*y] + V(((x^24 + x^16 + x^8 + 2)/x^2)*y), [(2/(x^10 + 2*x^2))*y] d[x] + V(((-1)/(x^10*y - x^2*y)) dx) + dV([(2/(x^10 + 2*x^2))*y])),
 ([(2*x^5/(x^8 + 2))*y] d[x] + V(((x^19 - x^11 + x^3)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]), [2/x^2*y] + V((2*x^19 + 2*x^11 + 2*x^3)*y), V((1/(x^5*y)) dx)),
 (V(((x^8 + 1)/y) dx), [2/x^3*y], [(1/(x^12 + 2*x^4))*y] d[x] + V(((-1)/(x^16*y - x^8*y)) dx) + dV([(1/(x^8 + 2))*y])),
 ([(x^3/(x^8 + 2))*y] d[x] + V(((x^13 + x^5)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]), [2/x^4*y] + V(((x^16 + x^8 + 1)/x^3)*y), [(2/(x^13 + 2*x^5))*y] d[x] + V(((-1)/(x^11*y - x^3*y)) dx) + dV([(2/(x^11 + 2*x^3))*y]))]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[1].omega8 + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l00.regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laB[0][?7h[?12l[?25h[?25l[?7luB[0][?7h[?12l[?25h[?25l[?7ltB[0][?7h[?12l[?25h[?25l[?7loB[0][?7h[?12l[?25h[?25l[?7lmB[0][?7h[?12l[?25h[?25l[?7l(B[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0, 0, 0)
aux (0, V(((2*x^11 + 2*x^10 + 2*x^8 + 2*x^7)/(x^35 + x^34 + x^32 + x^31 + x^27 + 2*x^25 + x^24 + 2*x^22 + x^19 + 2*x^16 + x^13 + 2*x^11 + x^10 + 2*x^8 + 2*x^4 + 2*x^3 + 2*x + 2))*y), V(((x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx))
aux_divided_by_p (0 dx, ((2*x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^4 - x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, ((2*x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^4 - x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
coord_aux_divided_by_p (0, 0, 0, 0, 0, 0, 0, 0)
[?7h[1, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l1]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l(1, 1, 0, 0, 0, 0, 0, 0)
aux (0, V(((x^11 + x^10 + x^8 + x^7)/(x^32 + x^31 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^25 + x^24 + 2*x^23 + x^22 + 2*x^21 + 2*x^20 + 2*x^18 + 2*x^17 + x^16 + 2*x^15 + 2*x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x + 1))*y), V(((x^10 + x^9 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (0 dx, ((x^3 + x^2)/(x^13 + 2*x^12 + 2*x^11 + x^10 + x^7 + 2*x^6 + 2*x^3 + x^2 + x + 2))*y, ((x^5 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, ((x^3 + x^2)/(x^13 + 2*x^12 + 2*x^11 + x^10 + x^7 + 2*x^6 + 2*x^3 + x^2 + x + 2))*y, ((x^5 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
coord_aux_divided_by_p (0, 0, 0, 0, 0, 0, 0, 0)
[?7h[1, 1, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l2]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B[2]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l(1, 2, 1, 0, 0, 0, 0, 0)
aux (V(((x^54 - x^46 + x^45 - x^37 - x^30 + x^22 - x^21 + x^13)/y) dx), V(((x^65 + x^64 + x^62 + x^61 + 2*x^41 + 2*x^40 + 2*x^38 + 2*x^37 + 2*x^14 + 2*x^13 + x^11 + x^10 + 2*x^8 + 2*x^7)/(x^35 + x^34 + x^32 + x^31 + x^27 + 2*x^25 + x^24 + 2*x^22 + x^19 + 2*x^16 + x^13 + 2*x^11 + x^10 + 2*x^8 + 2*x^4 + 2*x^3 + 2*x + 2))*y), V(((x^13 - x^12 + x^11 - x^10 + x^9 - x^8 - x^2 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^15 + x^12 - x^7 - x^4)/y) dx, ((x^21 + x^20 + 2*x^13 + 2*x^12 + 2*x^4 + x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^6 + x^5 + x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((x^15 + x^12 - x^7 - x^4)/y) dx, ((x^21 + x^20 + 2*x^13 + 2*x^12 + 2*x^4 + x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^6 + x^5 + x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
coord_aux_divided_by_p (0, 0, 0, 0, 2, 0, 0, 2)
[?7h[1, 2, 1, 0, 6, 0, 0, 6]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[2]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l(1, 0, 0, 1, 0, 0, 0, 0)
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [199], in <cell line: 1>()
----> 1 autom(B[Integer(3)]).coordinates(basis=B)

File <string>:102, in coordinates(self, basis)

File <string>:73, in coordinates(self)

File <string>:59, in coordinates(self)

File <string>:93, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l=autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lCautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l.autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lr autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ly autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ls autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lt autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7la autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ll autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ll autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7li autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ln autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7le autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l_ autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lc autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lh autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lh autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lm autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ll autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lg autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ly autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l_ autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lb autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lv autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7la autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7la autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ls autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7li autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ls autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l( autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l() autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l(); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:60, in __mul__(self, other)

File <string>:14, in __init__(self, C, g)

File <string>:224, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1310 if x_map is not None:
-> 1311     x_elt = (<Map>x_map)._call_(x)
   1312 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    410 S = R.base_ring()[tuple(Z)]
--> 411 ring = S[var]
    412 if not self:

File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
   1274         return self.list()[n]
-> 1275 return meth(n)
   1276 

File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
    630         raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
    634 # At this point, we have only handled the "names" keyword if it was
    635 # needed. Since we know the variable names, it would logically be
    636 # an error to specify an additional "names" keyword. However,
   (...)
    639 # and we allow this for historical reasons. However, the names
    640 # must be consistent!

File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
    899 
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
    901     r"""

File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
    992     # Convert names to strings and strip whitespace
--> 993     names = [str(x).strip() for x in names]
    994 else:

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2462, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular._repr_()
   2461 cdef ring *_ring = self._parent_ring
-> 2462 s = singular_polynomial_str(self._poly, _ring)
   2463 return s

File /ext/sage/9.7/src/sage/libs/singular/polynomial.pyx:442, in sage.libs.singular.polynomial.singular_polynomial_str()
    441 s = plusminus_pattern.sub("\\1 \\2 ", s)
--> 442 s = parenthvar_pattern.sub("\\1", s)
    443 return s

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/re.py:324, in _subx(pattern, template)
    322     return sre_parse.expand_template(template, match)
--> 324 def _subx(pattern, template):
    325     # internal: Pattern.sub/subn implementation helper
    326     template = _compile_repl(template, pattern)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(); autom(B[Integer(3)]).coordinates(basis=B)

File <string>:53, in crystalline_cohomology_basis(self, prec)

File <string>:24, in de_rham_witt_lift(cech_class, prec)

File <string>:6, in de_rham_witt_lift_form0(omega)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lr); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7le); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lc); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l ); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l=); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l ); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l2); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l0); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l0); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)

File <string>:52, in crystalline_cohomology_basis(self, prec)

File <string>:98, in de_rham_basis(self)

File <string>:80, in basis_de_rham_degrees(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:28, in __sub__(self, other)

File <string>:7, in __init__(self, C, g)

File <string>:259, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))
    710 try:
--> 711     return self._element_class(self, x, y, coerce=coerce)
    712 except TypeError:
    713     if parent(x) is parent(x0):

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
    336 """
    337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
--> 338     return repr(self.numer())
    339 else:
    340     numer_s = repr(self.numer())

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
is regular True True
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)

File <string>:102, in coordinates(self, basis)

File <string>:73, in coordinates(self)

File <string>:59, in coordinates(self)

File <string>:93, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2))*C.y[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2))*C.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 f = ((C.x**Integer(25) + C.x**Integer(24) + C.x**Integer(23) + C.x**Integer(22) + C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)))*C.y

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(



)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

(

))[?7h[?12l[?25h[?25l[?7l*))*C.y[?7h[?12l[?25h[?25l[?7lC))*C.y[?7h[?12l[?25h[?25l[?7l.))*C.y[?7h[?12l[?25h[?25l[?7lo))*C.y[?7h[?12l[?25h[?25l[?7ln))*C.y[?7h[?12l[?25h[?25l[?7le))*C.y[?7h[?12l[?25h[?25l[?7l(

(

))[?7h[?12l[?25h[?25l[?7l(



)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 f = ((C.x**Integer(25) + C.x**Integer(24) + C.x**Integer(23) + C.x**Integer(22) + C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)*C.one))*C.y

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(



)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

(

))[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l(

)(

)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l*)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 2*C
.

x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 2*
C

.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 2
*

C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lo)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 
2

*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7ln)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 +


2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 
+

 2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7luperelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lomega8 == om2[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.omega0.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7lf()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7ly()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 xi.coordinates()

File <string>:73, in coordinates(self)

File <string>:59, in coordinates(self)

File <string>:93, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l.

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lte[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 ((C.x**Integer(25) + C.x**Integer(24) + C.x**Integer(23) + C.x**Integer(22) + C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)*C.one))*C.y

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

 

 [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(, om1, f)

 

 [?7h[?12l[?25h[?25l[?7l.omega0.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l8infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lf.cordinates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 xi.coordinates()

File <string>:73, in coordinates(self)

File <string>:59, in coordinates(self)

File <string>:93, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 xi.coordinates()

File <string>:73, in coordinates(self)

File <string>:59, in coordinates(self)

File <string>:93, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(om.int())[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(om.int())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lin)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lxi)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f)

[?7h[?12l[?25h[?2004l[?7h(((x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2))*y,
 ((x^9 + 2*x^8 + x^7 + 2*x^5 + x^4 + 2*x^3 + x + 2)/(x^14 + 2*x^13 + x^11 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 2*x + 1))*y,
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.pth_root()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lsage: gg = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: gg

[?7h[?12l[?25h[?2004l[?7h(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l.(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lq(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lu(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lo(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l_(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lr(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7le(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lm(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)

[?7h[?12l[?25h[?2004l[?7h(x^10 + x^2 + 2*x, x^9 + x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + 2*x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: xi.f

[?7h[?12l[?25h[?2004l[?7h((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates(prec = 200)

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f.coordinates(prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates(prec = 500)

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgC.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lgC.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l=C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxi.f.function[?7h[?12l[?25h[?25l[?7lxi.f.function[?7h[?12l[?25h[?25l[?7lyxi.f.function[?7h[?12l[?25h[?25l[?7l(xi.f.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l=Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fffff = Fxy(xi.f.function)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fffff

[?7h[?12l[?25h[?2004l[?7h(x^25*y + x^24*y + x^23*y + x^22*y + x^21*y + x^20*y + x^19*y + x^18*y - x^16*y - x^15*y - x^14*y - x^13*y - x^12*y - x^11*y - x^10*y - x^9*y + x^8*y + x^7*y + x^6*y + x^5*y - x^4*y - x^3*y - x^2*y - x*y - y)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lnum[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff.numerator()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ld()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7lm()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: fffff.numerator().quo_rem(fffff.denominator())

[?7h[?12l[?25h[?2004l[?7h(x^10*y + x^2*y - x*y,
 x^9*y + x^8*y + x^7*y + x^6*y + x^5*y - x^4*y - x^3*y - x^2*y + x*y - y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7lfC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7lfC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7lfC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7lfC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7l C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7l=C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7l C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fffff = C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff = C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7lsage: fffff = C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff = C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: fffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y))/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

....:  C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lsage: fffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y))/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

....:  C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)

[?7h[?12l[?25h[?2004l  Input In [35]
    fffff = (C.x**Integer(9)*C.y + C.x**Integer(8)*C.y + C.x**Integer(7)*C.y + C.x**Integer(6)*C.y + C.x**Integer(5)*C.y - C.x**Integer(4)*C.y - C.x**Integer(3)*C.y - C.x**Integer(2)*C.y + C.x*C.y - C.y))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) - C.x**Integer(7) - C.x**Integer(6) - C.x**Integer(5) - C.x**Integer(4) - C.x**Integer(3) - C.x**Integer(2) - C.x - Integer(1))
                                                                                                                                                                                                           ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y))/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

....:  C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lsage: fffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +

....: C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 fffff = (C.x**Integer(9)*C.y + C.x**Integer(8)*C.y + C.x**Integer(7)*C.y + C.x**Integer(6)*C.y + C.x**Integer(5)*C.y - C.x**Integer(4)*C.y - C.x**Integer(3)*C.y - C.x**Integer(2)*C.y + C.x*C.y - C.y)/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) - C.x**Integer(7) - C.x**Integer(6) - C.x**Integer(5) - C.x**Integer(4) - C.x**Integer(3) - C.x**Integer(2) - C.x - Integer(1))

File <string>:50, in __sub__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +
 

....: C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l

 [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lsage: ffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.

 [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion

                     ffff.expansion         

 ffff.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 ffff.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 ffff.expansion         

 ffff.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffff.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^3 + t^13 + t^21 + O(t^23)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

 C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y

 [?7h[?12l[?25h[?25l[?7l.numerator().quo_rem(fffff.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=Cct_feld[?7h[?12l[?25h[?25l[?7lgg =C.x^9 +C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lxi.f.coordines(prec = 500)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

 

 [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9+ C.x^8+ 2*C.
x

^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^ + 2*C.x+ 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l))*C.y[?7h[?12l[?25h[?25l[?7lC

 

 [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lB =C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l); autom(B[3]).cordinates(bass=B)[?7h[?12l[?25h[?25l[?7lprec = 100); autm(B[3]).coordnates(basis=B)[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

 C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y

 [?7h[?12l[?25h[?25l[?7l.numerator().quo_rem(fffff.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=Cct_feld[?7h[?12l[?25h[?25l[?7lgg =C.x^9 +C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lxi.f.coordines(prec = 500)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

 

 [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l.coordinates()

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l = superelliptc((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

 

 [?7h[?12l[?25h[?25l[?7lf =((C.x^25 +C.x^24 +C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

 

 [?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lC =superelliptic((3 - x)^3 +x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7l = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l.coordinates()

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7lomega8.s_rgular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 1, 1, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f)

[?7h[?12l[?25h[?2004l[?7h((x^10 + x^2 + 2*x)*y,
 ((2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + x^2 + 2*x + 1)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y,
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

 

 [?7h[?12l[?25h[?25l[?7lC =superelliptic((3 - x)^3 +x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7l = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

 

 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

 C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lC.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y

 [?7h[?12l[?25h[?25l[?7l.numerator().quo_rem(fffff.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=Cct_feld[?7h[?12l[?25h[?25l[?7lgg =C.x^9 +C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lxi.f.coordines(prec = 500)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

 

 [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9+ C.x^8+ 2*C.
x

^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^ + 2*C.x+ 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l))*C.y[?7h[?12l[?25h[?25l[?7lC

 

 [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lB =C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l); autom(B[3]).cordinates(bass=B)[?7h[?12l[?25h[?25l[?7lprec = 100); autm(B[3]).coordnates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
is regular True True
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
[?7h[1, 3, 3, 1, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l(autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).coordinates(basi=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l4]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l(1, 1, 0, 2, 1, 2, 1, 2)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 autom(B[Integer(4)]).coordinates(basis=B)

File <string>:102, in coordinates(self, basis)

AttributeError: 'NoneType' object has no attribute 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrr = autom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lraise[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lValueError[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: raise ValueError("Test")

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 raise ValueError("Test")

ValueError: Test
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lraise ValueError("Test")[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lBC.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)

File <string>:107, in coordinates(self, basis)

File <string>:94, in div_by_p(self)

ValueError: aux.omega0.h2.function not in Rxy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Input In [58] in <cell line: 1>
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:20 in <module>

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:94
    raise ValueError("aux.omega0.h2.function not in Rxy":, aux.omega0.h2.function)
                                                        ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)

File <string>:107, in coordinates(self, basis)

File <string>:94, in div_by_p(self)

ValueError: ('aux.omega0.h2.function not in Rxy:', ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l - aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=omega8[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y)[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y)

[?7h[?12l[?25h[?2004l  Input In [62]
    om = ((Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(65) + C.x**Integer(64) + C.x**Integer(62) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(56) + C.x**Integer(55) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + Integer(2)*C.x**Integer(43) + Integer(2)*C.x**Integer(38) + C.x**Integer(37) + C.x**Integer(32) + Integer(2)*C.x**Integer(31) + Integer(2)*C.x**Integer(29) + C.x**Integer(28) + C.x**Integer(26) + Integer(2)*C.x**Integer(25) + C.x**Integer(23) + Integer(2)*C.x**Integer(22) + Integer(2)*C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + C.x)/(C.x**Integer(35) + Integer(2)*C.x**Integer(34) + Integer(2)*C.x**Integer(32) + C.x**Integer(31) + C.x**Integer(27) + Integer(2)*C.x**Integer(25) + Integer(2)*C.x**Integer(24) + C.x**Integer(22) + C.x**Integer(19) + C.x**Integer(16) + C.x**Integer(13) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + C.x**Integer(8) + C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x + Integer(1)))*C.y)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
 

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

 C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14


+ 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 om = ((Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(65) + C.x**Integer(64) + C.x**Integer(62) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(56) + C.x**Integer(55) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + Integer(2)*C.x**Integer(43) + Integer(2)*C.x**Integer(38) + C.x**Integer(37) + C.x**Integer(32) + Integer(2)*C.x**Integer(31) + Integer(2)*C.x**Integer(29) + C.x**Integer(28) + C.x**Integer(26) + Integer(2)*C.x**Integer(25) + C.x**Integer(23) + Integer(2)*C.x**Integer(22) + Integer(2)*C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + C.x)/(C.x**Integer(35) + Integer(2)*C.x**Integer(34) + Integer(2)*C.x**Integer(32) + C.x**Integer(31) + C.x**Integer(27) + Integer(2)*C.x**Integer(25) + Integer(2)*C.x**Integer(24) + C.x**Integer(22) + C.x**Integer(19) + C.x**Integer(16) + C.x**Integer(13) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + C.x**Integer(8) + C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x + Integer(1)))*C.y

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
 

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

 C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14


+ 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
 

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()

 

 

 [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = om.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lom = om.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l = om.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
 

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()

 

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.[?7h[?12l[?25h[?25l[?7lmom.[?7h[?12l[?25h[?25l[?7l1om.[?7h[?12l[?25h[?25l[?7l om.[?7h[?12l[?25h[?25l[?7l=om.[?7h[?12l[?25h[?25l[?7l om.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7l()p[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_root[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.pth_root()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lom1 = om.pth_root()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = om.pth_root()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.pth_rot()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = om1.pth_root()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [69], in <cell line: 1>()
----> 1 om1 = om1.pth_root()

File <string>:168, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om1.pth_root()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h((2*x^24 + x^23 + 2*x^21 + x^20 + 2*x^18 + x^17 + x^16 + 2*x^15 + x^14 + 2*x^12 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^5 + x^4 + 2*x^2 + x + 2)/(x^14 + 2*x^13 + x^11 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 2*x + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega.cartier().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^18 + x^10 + x^9 + x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: loa

[?7h[?12l[?25h[?2004l^[[C---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 loa

NameError: name 'loa' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.diffn().int()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status
On branch master
Your branch is up to date with 'origin/master'.

Changes not staged for commit:
  (use "git add <file>..." to update what will be committed)
  (use "git restore <file>..." to discard changes in working directory)
	modified:   sage/.run.term-0.term
	modified:   sage/drafty/draft.sage
	modified:   sage/init.sage
	modified:   sage/superelliptic/superelliptic_cech_class.sage
	modified:   sage/superelliptic/superelliptic_class.sage
	modified:   sage/superelliptic/superelliptic_form_class.sage
	modified:   sage/superelliptic_drw/automorphism.sage
	modified:   sage/superelliptic_drw/de_rham_witt_lift.sage
	modified:   sage/superelliptic_drw/decomposition_into_g0_g8.sage
	modified:   sage/superelliptic_drw/second_patch.sage
	modified:   sage/superelliptic_drw/superelliptic_drw_cech.sage
	modified:   sage/superelliptic_drw/superelliptic_drw_form.sage
	modified:   sage/tests.sage

Untracked files:
  (use "git add <file>..." to include in what will be committed)
	.crystalline_p2.ipynb.sage-jupyter2
	.deRhamComputation.ipynb.sage-jupyter2
	.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
	.git.x11-0.term
	.superelliptic.ipynb.sage-jupyter2
	.superelliptic_alpha.ipynb.sage-jupyter2
	.superelliptic_arbitrary_field.ipynb.sage-jupyter2
	git.x11
	sage/as_covers/tests/cartier_test.sage
	sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
	sage/drafty/2gpcovers.sage
	sage/drafty/as_cartier.sage
	sage/drafty/better_trace.sage
	sage/drafty/cartier_image_representation.sage
	sage/drafty/convert_superelliptic_into_AS.sage
	sage/drafty/draft4.sage
	sage/drafty/draft5.sage
	sage/drafty/draft6.sage
	sage/drafty/draft7.sage
	sage/drafty/draft8.sage
	sage/drafty/draft_klein_covers.sage
	sage/drafty/lift_to_de_rham.sage
	sage/drafty/pole_numbers.sage
	sage/superelliptic/frobenius_kernel.sage
	sage/superelliptic/tests/
	sage/superelliptic_drw/regular_form.sage
	sage/superelliptic_drw/tests/
	superelliptic_arbitrary_field.ipynb

no changes added to commit (use "git add" and/or "git commit -a")
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/as_covers/tests/cartier_test.sage sage/superelliptic_drw/tests/ sage/as_cosuperelliptic/tests/
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit = m-m ""w"s"p"o"l"r"z"e"d"n"i"e" "p"r"a"w"i"e" "d"z"[1@b[1@a[1@z[1@a[1@ [1@c[1@r[1@y[1@s[1@ [1@d[1@z[1@i[1@a[1@l[1@a[1@;[1@ [1@p[1@o[1@p[1@r[1@a[1@w[1@k[1@i[1@ [1@w[1@ [1@c[1@o[1@o[1@r[1@d[1@i[1@n[1@a[1@t[1@e[1@s[1@ [1@d[1@r[1@l[1@;[1@ [1@ [1@c[1@r[1@i[1@s[1@ i"a"l"a"j"a"
[master 42ccc4d] baza crys dziala; poprawki w coordinates dr; wspolrzednie cris prawie dzialaja
 20 files changed, 16269 insertions(+), 87 deletions(-)
 create mode 100644 sage/as_covers/tests/cartier_test.sage
 create mode 100644 sage/superelliptic/tests/a_number_test.sage
 create mode 100644 sage/superelliptic/tests/form_coordinates_test.sage
 create mode 100644 sage/superelliptic/tests/p_rank_test.sage
 create mode 100644 sage/superelliptic/tests/pth_root_test.sage
 create mode 100644 sage/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage
 create mode 100644 sage/superelliptic_drw/tests/superelliptic_drw_tests.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
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Delta compression using up to 4 threads
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Writing objects: 100% (30/30), 143.28 KiB | 1.06 MiB/s, done.
Total 30 (delta 18), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   ce0ac0d..42ccc4d  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sacd sa
bash: cd: sa: No such file or directory
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage/
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7llar_form()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7log.difn().regular_form()[?7h[?12l[?25h[?25l[?7lmg.difn().regular_form()[?7h[?12l[?25h[?25l[?7l g.difn().regular_form()[?7h[?12l[?25h[?25l[?7l=g.difn().regular_form()[?7h[?12l[?25h[?25l[?7l g.difn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om.dy = 0*C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.dy = 0*C.x[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lis_regular_on_U0()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx
m dx x^16
int(self) (2*x^12 + 2*x^10 + 2) dx
m dx x^12
int(self) (2*x^10 + 2) dx
m dx x^10
int(self) (2) dx
m dx 1
int(self) (0) dy
[?7hx^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g.function)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (g.function).quo_rem(y)

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2, x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l(g.function).quo_rem(y)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA(g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l=(g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7lsage: A = (g.function).quo_rem(y)[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = Rx(A)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = Rx(A)[?7h[?12l[?25h[?25l[?7l.omega.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.monomial_coefficient(x^3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 A.monomial_coefficient(x**Integer(3))

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient()
   6092 """
   6093 if not m.parent() is self._parent:
-> 6094     raise TypeError("monomial must have same parent as self.")
   6095 
   6096 d = m.degree()

TypeError: monomial must have same parent as self.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.monomial_coefficient(x^3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx^3)[?7h[?12l[?25h[?25l[?7lx^3)[?7h[?12l[?25h[?25l[?7l(x^3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: A.monomial_coefficient(Rx(x^3))

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.monomial_coefficient(Rx(x^3))[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: A.monomial_coefficient(Rx(x^3))

  A.abs                         A.all_roots_in_interval       A.base_ring                   A.change_variable_name        A.compose_trunc                

  A.adams_operator              A.any_root                    A.cartesian_product           A.coefficients                A.composed_op                  

  A.add_bigoh                   A.args                        A.category                    A.complex_roots               A.constant_coefficient        >

  A.additive_order              A.base_extend                 A.change_ring                 A.compose_power               A.content_ideal                

 [?7h[?12l[?25h[?25l[?7labs

 A.abs                        







 <unknown> [?7h[?12l[?25h[?25l[?7lll_roots_in_interval

 A.abs                         A.all_roots_in_interval      [?7h[?12l[?25h[?25l[?7lbase_ring

 A.all_roots_in_interval       A.base_ring                  [?7h[?12l[?25h[?25l[?7lchange_variable_name

 A.base_ring                   A.change_variable_name       [?7h[?12l[?25h[?25l[?7lompose_tunc

 A.change_variable_name        A.compose_trunc              [?7h[?12l[?25h[?25l[?7lycltomic_part

 ll_roots_in_intervalbase_ring            change_variable_nameompose_tunc       ycltomic_part

 ny_rot      cartesian_productoefficients     mposed_op degree     

<rgs     categoryomplex_rootsnstant_cefficientdeomiator         

 base_extend   chang_rigompose_powerntentidealderivaive   [?7h[?12l[?25h[?25l[?7ldit

base_ring            change_variable_nameompose_tunc       ycltomic_partdit           

cartesian_productoefficients     mposed_op degree     iff  

categoryomplex_rootsnstant_cefficientdeomiator         iffereniate

chang_rigompose_powerntentidealderivaive   iscrimnant[?7h[?12l[?25h[?25l[?7lspersion

change_variable_nameompose_tunc       ycltomic_partdit           spersion

oefficients     mposed_op degree     iff  spersion_set

omplex_rootsnstant_cefficientdeomiator         iffereniatevides      

ompose_powerntentidealderivaive   iscrimnantump        [?7h[?12l[?25h[?25l[?7lums

ompose_tunc       ycltomic_partdit           spersionums     

mposed_op degree     iff  spersion_seteuclidean_degree

nstant_cefficientdeomiator         iffereniatevides      exponnts

ntentidealderivaive   iscrimnantump        factor[?7h[?12l[?25h[?25l[?7lgcd

ycltomic_partdit           spersionums     gcd  

degree     iff  spersion_seteuclidean_degreeget_cparent     

deomiator         iffereniatevides      exponntsglobal_height

derivaive   iscrimnantump        factorgradient[?7h[?12l[?25h[?25l[?7lhamming_weight

dit           spersionums     gcd  hamming_weight

iff  spersion_seteuclidean_degreeget_cparent     hasyclotomic_factor

iffereniatevides      exponntsglobal_heighthomogenize   

iscrimnantump        factorgradientintegral[?7h[?12l[?25h[?25l[?7linversemod

spersionums     gcd  hamming_weightinversemod   

spersion_seteuclidean_degreeget_cparent     hasyclotomic_factorinverse_f_unit      

vides      exponntsglobal_heighthomogenize   inverse_sries_trunc

ump        factorgradientintegrals_constant[?7h[?12l[?25h[?25l[?7ls_cyclotmic

ums     gcd  hamming_weightinversemod   s_cyclotmic

euclidean_degreeget_cparent     hasyclotomic_factorinverse_f_unit      s_cyclotomic_product

exponntsglobal_heighthomogenize   inverse_sries_truncs_gen              

factorgradientintegrals_constanthmogeeous[?7h[?12l[?25h[?25l[?7lidempotent

gcd  hamming_weightinversemod   s_cyclotmicidempotent

get_cparent     hasyclotomic_factorinverse_f_unit      s_cyclotomic_productirreducible       

global_heighthomogenize   inverse_sries_truncs_gen              moic

gradientintegrals_constanthmogeeousmnmial   [?7h[?12l[?25h[?25l[?7lnilpotent

hamming_weightinversemod   s_cyclotmicidempotentnilpotent 

hasyclotomic_factorinverse_f_unit      s_cyclotomic_productirreducible       one        

homogenize   inverse_sries_truncs_gen              moicprime

integrals_constanthmogeeousmnmial   primitive[?7h[?12l[?25h[?25l[?7lreal_rooed

inversemod   s_cyclotmicidempotentnilpotent real_rooed

inverse_f_unit      s_cyclotomic_productirreducible       one        square

inverse_sries_truncs_gen              moicprimesquarefree

s_constanthmogeeousmnmial   primitiveter     [?7h[?12l[?25h[?25l[?7lunit

s_cyclotmicidempotentnilpotent real_rooedunit       

s_cyclotomic_productirreducible       one        squareweil_polynomial

s_gen              moicprimesquarefreezero      

hmogeeousmnmial   primitiveter     lc     [?7h[?12l[?25h[?25l[?7llcm

idempotentnilpotent real_rooedunit       lcm    

irreducible       one        squareweil_polynomialleadingcefficent

moicprimesquarefreezero      list   

mnmial   primitiveter     lc     m[?7h[?12l[?25h[?25l[?7local_height

nilpotent real_rooedunit       lcm    ocal_height

one        squareweil_polynomialleadingcefficentocal_height_arch  

primesquarefreezero      list   t  

primitiveter     lc     mmap_coefficients[?7h[?12l[?25h[?25l[?7lmd

real_rooedunit       lcm    ocal_heightmd         

squareweil_polynomialleadingcefficentocal_height_arch  mnic            

squarefreezero      list   t  monomial_coefficient

ter     lc     mmap_coefficientsonomials       [?7h[?12l[?25h[?25l[?7lultiplication_trunc

unit       lcm    ocal_heightmd         ultiplication_trunc

weil_polynomialleadingcefficentocal_height_arch  mnic            ultiplicative_order

zero      list   t  monomial_coefficientn                   

lc     mmap_coefficientsonomials       newton_raphson[?7h[?12l[?25h[?25l[?7lod

 A.mod                         A.multiplication_trunc       [?7h[?12l[?25h[?25l[?7llcal_height

 A.local_height                A.mod                        [?7h[?12l[?25h[?25l[?7lcm

 A.lcm                         A.local_height               [?7h[?12l[?25h[?25l[?7leading_coefficient

 A.lcm                        

 A.leading_coefficient        [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.leading_coefficient()

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lA.leading_coefficient()[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^2 + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega8_lift0.omega8 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
[?7h((x^20 + x^18 + 2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2 + 2)/x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
[?7h((-x^18 + x^12 - x^6 + x^4 + x^2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7l() == om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om.form()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed (x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y
((x^20 + x^18 + 2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2 + 2)/x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [27], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:48, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [29], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:49, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:49, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
n_lead, f_lead, (2*a + r) 1 1 11
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:50, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
n_lead, f_lead, (2*a + r) 1 1 11
W_coeff 2
W 2*x^4
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [35], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:46, in int(self)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'leading_coefficient'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
n_lead, f_lead, (2*a + r) 1 1 11
W_coeff 2
W 2*x^4
n_lead, f_lead, (2*a + r) 1 1 7
W_coeff 1
W 2*x^4 + x^2
n_lead, f_lead, (2*a + r) 1 1 3
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [37], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:50, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    372     z = <Integer>value
    373 elif isinstance(value, rational.Rational):
--> 374     z = value % self.__modulus.sageInteger
    375 elif integer_check_long_py(value, &longval, &err) and not err:
    376     self.set_from_long(longval)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
   2823 n = rat.numer() % other
   2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
   2826 return (n * d) % other
   2827 

File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
   6772 sig_off()
   6773 if r == 0:
-> 6774     raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
   6775 return ans
   6776 

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
numerator x^6 + x^4 + x^2 + 1
W 2*x^4
numerator x^4 + x^2 + 1
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:50, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    372     z = <Integer>value
    373 elif isinstance(value, rational.Rational):
--> 374     z = value % self.__modulus.sageInteger
    375 elif integer_check_long_py(value, &longval, &err) and not err:
    376     self.set_from_long(longval)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
   2823 n = rat.numer() % other
   2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
   2826 return (n * d) % other
   2827 

File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
   6772 sig_off()
   6773 if r == 0:
-> 6774     raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
   6775 return ans
   6776 

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
 

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lC.y/C.x).diffn()

 

 

 [?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om = (C.x^2 + C.one)/C.y * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lom = (C.x^2 + C.one)/C.y * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().diffn() == omform()[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l = (C.x^2 + C.one)/C.y * C.dx[?7h[?12l[?25h[?25l[?7lg = C.x^7 *C.y^8 + 2*C.xC.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx
W 0
numerator x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx
W 2*x^4
numerator x^4 + x^2 + 1
(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    372     z = <Integer>value
    373 elif isinstance(value, rational.Rational):
--> 374     z = value % self.__modulus.sageInteger
    375 elif integer_check_long_py(value, &longval, &err) and not err:
    376     self.set_from_long(longval)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
   2823 n = rat.numer() % other
   2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
   2826 return (n * d) % other
   2827 

File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
   6772 sig_off()
   6773 if r == 0:
-> 6774     raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
   6775 return ans
   6776 

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() (x/y) dx
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    372     z = <Integer>value
    373 elif isinstance(value, rational.Rational):
--> 374     z = value % self.__modulus.sageInteger
    375 elif integer_check_long_py(value, &longval, &err) and not err:
    376     self.set_from_long(longval)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
   2823 n = rat.numer() % other
   2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
   2826 return (n * d) % other
   2827 

File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
   6772 sig_off()
   6773 if r == 0:
-> 6774     raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
   6775 return ans
   6776 

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() (x/y) dx
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    372     z = <Integer>value
    373 elif isinstance(value, rational.Rational):
--> 374     z = value % self.__modulus.sageInteger
    375 elif integer_check_long_py(value, &longval, &err) and not err:
    376     self.set_from_long(longval)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
   2823 n = rat.numer() % other
   2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
   2826 return (n * d) % other
   2827 

File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
   6772 sig_off()
   6773 if r == 0:
-> 6774     raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
   6775 return ans
   6776 

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:52, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    454         x = x.numerator() * x.denominator().inverse_of_unit()
    455     else:
--> 456         raise TypeError("denominator must be a unit")
    457 elif isinstance(x, pari_gen):
    458     if x.type() == 't_RFRAC':

TypeError: denominator must be a unit
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
W_coeff 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
W_coeff 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
W_coeff 2
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:53, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    454         x = x.numerator() * x.denominator().inverse_of_unit()
    455     else:
--> 456         raise TypeError("denominator must be a unit")
    457 elif isinstance(x, pari_gen):
    458     if x.type() == 't_RFRAC':

TypeError: denominator must be a unit
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
a -2
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

File <string>:53, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    454         x = x.numerator() * x.denominator().inverse_of_unit()
    455     else:
--> 456         raise TypeError("denominator must be a unit")
    457 elif isinstance(x, pari_gen):
    458     if x.type() == 't_RFRAC':

TypeError: denominator must be a unit
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lint().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form().int()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr_form().int()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 om.regular_form().int()

AttributeError: 'superelliptic_function' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint().difn() == om.form()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ldiffn() == om.form()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om.form()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 +2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l().diffn() == om.form()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() == om.form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l om.form()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om.form()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgom.int()[?7h[?12l[?25h[?25l[?7l om.int()[?7h[?12l[?25h[?25l[?7l-om.int()[?7h[?12l[?25h[?25l[?7l om.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g - om.int()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

....: sage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [66], in <cell line: 2>()
      1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2))
----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)

File <string>:107, in coordinates(self, basis)

File <string>:94, in div_by_p(self)

ValueError: ('aux.omega0.h2.function not in Rxy:', ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lfff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
 

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()

 

 

 [?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.pth_root()

[?7h[?12l[?25h[?2004l[?7h((2*x^24 + x^23 + 2*x^21 + x^20 + 2*x^18 + x^17 + x^16 + 2*x^15 + x^14 + 2*x^12 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^5 + x^4 + 2*x^2 + x + 2)/(x^14 + 2*x^13 + x^11 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 2*x + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition

 decomposition                 decomposition_g0_g8_pth_power

 decomposition_g0_g8           decomposition_omega0_omega8  





 [?7h[?12l[?25h[?25l[?7l_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7l

 decomposition                



 <unknown> [?7h[?12l[?25h[?25l[?7l_g0_g8_pth_power

 decomposition                 decomposition_g0_g8_pth_power[?7h[?12l[?25h[?25l[?7lomea0_omega8

 decomposition_g0_g8_pth_power

 decomposition_omega0_omega8  [?7h[?12l[?25h[?25l[?7lg0_8



 decomposition_g0_g8           decomposition_omega0_omega8  [?7h[?12l[?25h[?25l[?7l

 decomposition                

 decomposition_g0_g8          [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lff.pth_root()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 -x)^3 + x^3- x, 2)

B = C.crystalline_cohomology_basis(prec = 100);autom(B[3]).coordinates(basis=B)

 

 [?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()



....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()

B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

 [?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
h2 ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^53 + x^52 + 2*x^50 + 2*x^49 + x^47 + x^46 + 2*x^44 + 2*x^43 + x^41 + x^40 + 2*x^38 + 2*x^37 + x^35 + x^34 + 2*x^32 + 2*x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + 2*x^20 + 2*x^19 + x^17 + x^16 + x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^17 + 2*x^16 + x^15 + 2*x^14 + x^13 + 2*x^12 + x^11 + 2*x^10 + x^9 + x^8 + x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 2*x + 2)/(x^7 + 2*x^6 + x^5 + 2*x^4 + x^3 + 2*x^2 + x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
is regular True True
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
[?7h[4, 3, 3, 1, 0, 0, 3, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l(autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()autom(B[3]).coordinates(basis=B)

 [?7h[?12l[?25h[?25l[?7l(autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l(autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l4]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l(1, 1, 0, 2, 1, 2, 1, 2)
h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [72], in <cell line: 1>()
----> 1 autom(B[Integer(4)]).coordinates(basis=B)

File <string>:114, in coordinates(self, basis)

File <string>:99, in div_by_p(self)

ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l4]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y
aux.omega8.h2 ((2*x^30 + x^24 + 2*x^21 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x + 1)/(x^27 + x^19 + x^11))*y
second_patch(aux.omega8.h2.diffn()).is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [74], in <cell line: 2>()
      1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2))
----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:116, in coordinates(self, basis)

File <string>:101, in div_by_p(self)

ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_nfty[?7h[?12l[?25h[?25l[?7lx.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + O(t^18)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lyx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + O(t^11)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - om.int()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = C.genus()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()_[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^(g+1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: u.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^2 + 2*t^18 + O(t^22)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: v.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^5 +

....: 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^5 
+

 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7lg((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^5


+ 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7l ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^
5

 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7l=((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x
^

5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7l ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
x

^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
x

....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^11))*C.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 gg = ((Integer(2)*C.x**Integer(30) + C.x**Integer(24) + Integer(2)*C.x**Integer(21) + Integer(2)*C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(15) + C.x**Integer(14) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + C.x**Integer(10) + Integer(2)*C.x**Integer(9) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(1))/(C.x**Integer(27) + C.x**Integer(19) + C.x**Integer(11)))*C.y

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
x

....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(

)()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7lon)/(C.x^27+ C.x^19+ C.x^11))*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
x

....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + C.one)/(C.x^27 + C.x^19 + C.x^11))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.pth_root()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
x

....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + C.one)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.pth_root()

 [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^10 + t^12 + 2*t^16 + O(t^20)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lgg.iffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpasion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
x

....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + C.one)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7l1)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()

 [?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7lggenus()[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = suerelliptic((x^3 - x)^3 + x^3 - x, 2)

....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y
aux.omega8.omega ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
aux.omega8.h2 ((2*x^30 + x^24 + 2*x^21 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x + 1)/(x^27 + x^19 + x^11))*y
second_patch(aux.omega8.h2.diffn()).is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [87], in <cell line: 2>()
      1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2))
----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:117, in coordinates(self, basis)

File <string>:102, in div_by_p(self)

ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.x^2 + C.one)/Cy * C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - 1)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^
9

....: *C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - 1)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^
9

....: *C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [88], in <cell line: 1>()
----> 1 om = ((C.x**Integer(28) - C.x**Integer(26) + C.x**Integer(25) - C.x**Integer(24) + C.x**Integer(23) - C.x**Integer(22) - C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(15) - C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) - C.x**Integer(10) - C.x**Integer(8) - C.x**Integer(7) + C.x**Integer(6) - C.x**Integer(5) + C.x**Integer(4) + C.x**Integer(2) + C.x - Integer(1))/(C.x**Integer(16)*C.y - C.x**Integer(15)*C.y + C.x**Integer(14)*C.y - C.x**Integer(13)*C.y + C.x**Integer(12)*C.y - C.x**Integer(11)*C.y + C.x**Integer(10)*C.y - C.x**Integer(9)*C.y - C.x**Integer(8)*C.y + C.x**Integer(7)*C.y - C.x**Integer(6)*C.y + C.x**Integer(5)*C.y - C.x**Integer(4)*C.y + C.x**Integer(3)*C.y - C.x**Integer(2)*C.y + C.x*C.y))*C.dx

File <string>:50, in __sub__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - 1)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^
9

....: *C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int)diffn() == om.form()

 

 [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion

 om.expansion         

                   om.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 om.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 om.expansion         

 om.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + O(t^-8)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h((x^13 - x^12 - x^11 - x^10 - x^9 + x^8 - x^5 + x^4 - x^3 - x^2 + x - 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: lau.

  lau.O                      lau.additive_order         lau.category               lau.common_valuation       lau.dump                    

  lau.V                      lau.base_extend            lau.change_ring            lau.degree                 lau.dumps                   

  lau.abs                    lau.base_ring              lau.coefficients           lau.denominator            lau.euclidean_degree       >

  lau.add_bigoh              lau.cartesian_product      lau.common_prec            lau.derivative             lau.exponents               

 [?7h[?12l[?25h[?25l[?7lO

 lau.O                     







 <unknown> [?7h[?12l[?25h[?25l[?7ladditive_order

 lau.O                      lau.additive_order        [?7h[?12l[?25h[?25l[?7lcategory

 lau.additive_order         lau.category              [?7h[?12l[?25h[?25l[?7lommon_valuation

 lau.category               lau.common_valuation      [?7h[?12l[?25h[?25l[?7ldup

 lau.common_valuation       lau.dump                  [?7h[?12l[?25h[?25l[?7lfactor

 additive_ordercategory      ommon_valuationdup            factor

 base_extendchang_rigdegre     umps gcd  

<bae_ringcoefficientsdenomnator eucliden_degreeintegral        

 cartesian_productommon_prec      derivativ exponents inverse  [?7h[?12l[?25h[?25l[?7linverse_of_unit

category      ommon_valuationdup            factorinverse_of_unit

chang_rigdegre     umps gcd  is_idempotent

coefficientsdenomnator eucliden_degreeintegral        s_monomial

ommon_prec      derivativ exponents inverse  s_nilpotent[?7h[?12l[?25h[?25l[?7ls_one

ommon_valuationdup            factorinverse_of_units_one         

degre     umps gcd  is_idempotentprie     

denomnator eucliden_degreeintegral        s_monomialunit    

derivativ exponents inverse  s_nilpotentzero     [?7h[?12l[?25h[?25l[?7llaurent_polynomial

dup            factorinverse_of_units_one         laurent_polynomial

umps gcd  is_idempotentprie     lcm     

eucliden_degreeintegral        s_monomialunit    lift_to_precision

exponents inverse  s_nilpotentzero     list   [?7h[?12l[?25h[?25l[?7lmultiplicative_order

factorinverse_of_units_one         laurent_polynomialmultiplicative_order

gcd  is_idempotentprie     lcm     n  

integral        s_monomialunit    lift_to_precisionnth_rot         

inverse  s_nilpotentzero     list   numerator[?7h[?12l[?25h[?25l[?7llaurent_polynomial

 lau.laurent_polynomial     lau.multiplicative_order  [?7h[?12l[?25h[?25l[?7lmultiplicative_order

 lau.laurent_polynomial     lau.multiplicative_order  [?7h[?12l[?25h[?25l[?7lnmerical_approx

inverse_of_units_one         laurent_polynomialmultiplicative_ordernmerical_approx    

is_idempotentprie     lcm     n  order

s_monomialunit    lift_to_precisionnth_rot         parent  

s_nilpotentzero     list   numeratorpow_seies[?7h[?12l[?25h[?25l[?7lpows

s_one         laurent_polynomialmultiplicative_ordernmerical_approx    pows          

prie     lcm     n  orderpec 

unit    lift_to_precisionnth_rot         parent  recision_absolute

zero     list   numeratorpow_seiesrecision_relative[?7h[?12l[?25h[?25l[?7lquo_em

laurent_polynomialmultiplicative_ordernmerical_approx    pows          quo_em

lcm     n  orderpec radical

lift_to_precisionnth_rot         parent  recision_absoluterename            

list   numeratorpow_seiesrecision_relativereset_name        [?7h[?12l[?25h[?25l[?7lresidue

multiplicative_ordernmerical_approx    pows          quo_emresidue

n  orderpec radicaleverse

nth_rot         parent  recision_absoluterename            save  

numeratorpow_seiesrecision_relativereset_name        shif     [?7h[?12l[?25h[?25l[?7lsquarefree_part

nmerical_approx    pows          quo_emresiduesquarefree_part

orderpec radicaleversesubs   

parent  recision_absoluterename            save  ubstitute

pow_seiesrecision_relativereset_name        shif     truncate[?7h[?12l[?25h[?25l[?7ltrncate_laurentseries

pows          quo_emresiduesquarefree_parttrncate_laurentseries

pec radicaleversesubs   truncate_neg

recision_absoluterename            save  ubstitutevaluation 

recision_relativereset_name        shif     truncatevaluation_zero_part[?7h[?12l[?25h[?25l[?7lvariabl

quo_emresiduesquarefree_parttrncate_laurentseriesvariabl               

radicaleversesubs   truncate_negvershibun 

rename            save  ubstitutevaluation xgcd      

reset_name        shif     truncatevaluation_zero_part                            [?7h[?12l[?25h[?25l[?7ltruncat_laurentseries

 lau.truncate_laurentseries lau.variable              [?7h[?12l[?25h[?25l[?7l

 lau.truncate_laurentseries





 lau.truncate              [?7h[?12l[?25h[?25l[?7lshift







 lau.shift                  lau.truncate              [?7h[?12l[?25h[?25l[?7lrese_name







 lau.reset_name             lau.shift                 [?7h[?12l[?25h[?25l[?7lprecision_relative

powes quo_remresidue        sqarefree_part       truncat_laurentseries 

prec   adicalreversesubs        trunat_ne 

precision_absoluterenameave      substitutevaluation>

precision_relativerese_nameshift   truncate            lau.valuation_zero_part    [?7h[?12l[?25h[?25l[?7lower_series

numical_approxpowes quo_remresidue        sqarefree_part       

oderprec   adicalreversesubs        

arent            precision_absoluterenameave      substitute

ower_series      precision_relativerese_nameshift   truncate           [?7h[?12l[?25h[?25l[?7lnumato

mltiplicative_ordernumical_approxpowes quo_remresidue        

n    oderprec   adicalreverse

nth_rootarent            precision_absoluterenameave      

numato   ower_series      precision_relativerese_nameshift   [?7h[?12l[?25h[?25l[?7llist

laurent_polynomial  mltiplicative_ordernumical_approxpowes quo_rem

lcmn    oderprec   adical

lift_t_precisionnth_rootarent            precision_absoluterename

list     numato   ower_series      precision_relativerese_name[?7h[?12l[?25h[?25l[?7lis_zero

is_one            laurent_polynomial  mltiplicative_ordernumical_approxpowes 

is_primelcmn    oderprec   

is_unit          lift_t_precisionnth_rootarent            precision_absolute

is_zerolist     numato   ower_series      precision_relative[?7h[?12l[?25h[?25l[?7lnilpotent

nverse_of_unitis_one            laurent_polynomial  mltiplicative_ordernumical_approx

idepotentis_primelcmn    oder

monomialis_unit          lift_t_precisionnth_rootarent            

nilpotentis_zerolist     numato   ower_series      [?7h[?12l[?25h[?25l[?7lnverse

factor         nverse_of_unitis_one            laurent_polynomial  mltiplicative_order

gcd          idepotentis_primelcmn    

ntegral   monomialis_unit          lift_t_precisionnth_root

nverse     nilpotentis_zerolist     numato   [?7h[?12l[?25h[?25l[?7lexponents

dump  factor         nverse_of_unitis_one            laurent_polynomial  

dumpsgcd          idepotentis_primelcm

euclidean_degreentegral   monomialis_unit          lift_t_precision

exponentsnverse     nilpotentis_zerolist     [?7h[?12l[?25h[?25l[?7lderivative

comon_valuationdump  factor         nverse_of_unitis_one            

egreedumpsgcd          idepotentis_prime

denomintor     euclidean_degreentegral   monomialis_unit          

derivativeexponentsnverse     nilpotentis_zero[?7h[?12l[?25h[?25l[?7lcommon_prc

ategory        comon_valuationdump  factor         nverse_of_unit

chang_ringegreedumpsgcd          idepotent

coeffcientsdenomintor     euclidean_degreentegral   monomial

common_prcderivativeexponentsnverse     nilpotent[?7h[?12l[?25h[?25l[?7lartesian_product

additive_orderategory        comon_valuationdump  factor         

base_xtedchang_ringegreedumpsgcd          

base_ring   coeffcientsdenomintor     euclidean_degreentegral   

artesian_productcommon_prcderivativeexponentsnverse     [?7h[?12l[?25h[?25l[?7ladd_bigoh

 O             additive_orderategory        comon_valuationdump  

 V          base_xtedchang_ringegreedumps

 ab      base_ring   coeffcientsdenomintor     euclidean_degree

 add_bigoh        artesian_productcommon_prcderivativeexponents[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lcate

 lau.truncate              

 lau.truncate_laurentseries

 lau.truncate_neg          [?7h[?12l[?25h[?25l[?7l

 lau.truncate              





 <unknown> [?7h[?12l[?25h[?25l[?7l_laurentseries

 lau.truncate              

 lau.truncate_laurentseries[?7h[?12l[?25h[?25l[?7lneg



 lau.truncate_laurentseries

 lau.truncate_neg          [?7h[?12l[?25h[?25l[?7l





 lau.truncate_neg          

[?7h[?12l[?25h[?25l[?7l_neg





 lau.truncate_neg          

 <unknown> [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.truncate_neg()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [94], in <cell line: 1>()
----> 1 lau.truncate_neg()

TypeError: LaurentSeries.truncate_neg() takes exactly one argument (0 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.truncate_neg()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lau.truncate_neg(3)

[?7h[?12l[?25h[?2004l[?7hO(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.truncate_neg(3)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.truncate_neg(3)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lent_polynomial[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.laurent_polynomial()

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.laurent_polynomial()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: lau.laurent_polynomial()

  lau.O                      lau.additive_order         lau.category               lau.common_valuation       lau.dump                    

  lau.V                      lau.base_extend            lau.change_ring            lau.degree                 lau.dumps                   

  lau.abs                    lau.base_ring              lau.coefficients           lau.denominator            lau.euclidean_degree       >

  lau.add_bigoh              lau.cartesian_product      lau.common_prec            lau.derivative             lau.exponents               

 [?7h[?12l[?25h[?25l[?7lO

 lau.O                     







 <unknown> [?7h[?12l[?25h[?25l[?7ladditive_order

 lau.O                      lau.additive_order        [?7h[?12l[?25h[?25l[?7lcategory

 lau.additive_order         lau.category              [?7h[?12l[?25h[?25l[?7lommon_valuation

 lau.category               lau.common_valuation      [?7h[?12l[?25h[?25l[?7lategory

 lau.category               lau.common_valuation      [?7h[?12l[?25h[?25l[?7lhane_ring

 lau.category              

 lau.change_ring           [?7h[?12l[?25h[?25l[?7ldegre



 lau.change_ring            lau.degree                [?7h[?12l[?25h[?25l[?7lumps



 lau.degree                 lau.dumps                 [?7h[?12l[?25h[?25l[?7legree



 lau.degree                 lau.dumps                 [?7h[?12l[?25h[?25l[?7lcommon_valuation

 lau.common_valuation      

 lau.degree                [?7h[?12l[?25h[?25l[?7ldup

 lau.common_valuation       lau.dump                  [?7h[?12l[?25h[?25l[?7ls

 lau.dump                  

 lau.dumps                 [?7h[?12l[?25h[?25l[?7leclidean_degree



 lau.dumps                 

 lau.euclidean_degree      [?7h[?12l[?25h[?25l[?7lxponents





 lau.euclidean_degree      

 lau.exponents             [?7h[?12l[?25h[?25l[?7linverse

 additive_ordercategory      ommon_valuationdup            factor

 base_extendchang_rigdegre     umps gcd  

<bae_ringcoefficientsdenomnator eucliden_degreeintegral        

 cartesian_productommon_prec      derivativ exponents inverse  [?7h[?12l[?25h[?25l[?7ltgral





 lau.integral              

 lau.inverse               [?7h[?12l[?25h[?25l[?7lgcd



 lau.gcd                   

 lau.integral              [?7h[?12l[?25h[?25l[?7lfactor

 lau.factor                

 lau.gcd                   [?7h[?12l[?25h[?25l[?7lgcd

 lau.factor                

 lau.gcd                   [?7h[?12l[?25h[?25l[?7lintegral



 lau.gcd                   

 lau.integral              [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [98], in <cell line: 1>()
----> 1 lau.integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lau.

  lau.O                      lau.additive_order         lau.category               lau.common_valuation       lau.dump                    

  lau.V                      lau.base_extend            lau.change_ring            lau.degree                 lau.dumps                   

  lau.abs                    lau.base_ring              lau.coefficients           lau.denominator            lau.euclidean_degree       >

  lau.add_bigoh              lau.cartesian_product      lau.common_prec            lau.derivative             lau.exponents               

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lO

 lau.O                     







 <unknown> [?7h[?12l[?25h[?25l[?7ladditive_order

 lau.O                      lau.additive_order        [?7h[?12l[?25h[?25l[?7lcategory

 lau.additive_order         lau.category              [?7h[?12l[?25h[?25l[?7lommon_valuation

 lau.category               lau.common_valuation      [?7h[?12l[?25h[?25l[?7ldup

 lau.common_valuation       lau.dump                  [?7h[?12l[?25h[?25l[?7lfactor

 additive_ordercategory      ommon_valuationdup            factor

 base_extendchang_rigdegre     umps gcd  

<bae_ringcoefficientsdenomnator eucliden_degreeintegral        

 cartesian_productommon_prec      derivativ exponents inverse  [?7h[?12l[?25h[?25l[?7linverse_of_unit

category      ommon_valuationdup            factorinverse_of_unit

chang_rigdegre     umps gcd  is_idempotent

coefficientsdenomnator eucliden_degreeintegral        s_monomial

ommon_prec      derivativ exponents inverse  s_nilpotent[?7h[?12l[?25h[?25l[?7lfactor

 lau.factor                 lau.inverse_of_unit       [?7h[?12l[?25h[?25l[?7lgcd

 lau.factor                

 lau.gcd                   [?7h[?12l[?25h[?25l[?7lintegral



 lau.gcd                   

 lau.integral              [?7h[?12l[?25h[?25l[?7ls_monomial





 lau.integral               lau.is_monomial           [?7h[?12l[?25h[?25l[?7lidempotent



 lau.is_idempotent         

 lau.is_monomial           [?7h[?12l[?25h[?25l[?7lnverse_f_unit

 lau.inverse_of_unit       

 lau.is_idempotent         [?7h[?12l[?25h[?25l[?7ls_one

ommon_valuationdup            factorinverse_of_units_one         

degre     umps gcd  is_idempotentprie     

denomnator eucliden_degreeintegral        s_monomialunit    

derivativ exponents inverse  s_nilpotentzero     [?7h[?12l[?25h[?25l[?7lprime

 lau.is_one                

 lau.is_prime              [?7h[?12l[?25h[?25l[?7llcm

dup            factorinverse_of_units_one         laurent_polynomial

umps gcd  is_idempotentprie     lcm     

eucliden_degreeintegral        s_monomialunit    lift_to_precision

exponents inverse  s_nilpotentzero     list   [?7h[?12l[?25h[?25l[?7laurent_polynomial

 lau.laurent_polynomial    

 lau.lcm                   [?7h[?12l[?25h[?25l[?7lcm

 lau.laurent_polynomial    

 lau.lcm                   [?7h[?12l[?25h[?25l[?7lift_to_precision



 lau.lcm                   

 lau.lift_to_precision     [?7h[?12l[?25h[?25l[?7ls





 lau.lift_to_precision     

 lau.list                  [?7h[?12l[?25h[?25l[?7lf_to_precision





 lau.lift_to_precision     

 lau.list                  [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.lift_to_precision(0)

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7llau.lift_to_precision(0)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

  lau.O                      lau.additive_order         lau.category               lau.common_valuation       lau.dump                    

  lau.V                      lau.base_extend            lau.change_ring            lau.degree                 lau.dumps                   

            lau.abs                    lau.base_ring              lau.coefficients           lau.denominator            lau.euclidean_degree       >

  lau.add_bigoh              lau.cartesian_product      lau.common_prec            lau.derivative             lau.exponents               

 [?7h[?12l[?25h[?25l[?7lO

 lau.O                     







 <unknown> [?7h[?12l[?25h[?25l[?7ladditive_order

 lau.O                      lau.additive_order        [?7h[?12l[?25h[?25l[?7lcategory

 lau.additive_order         lau.category              [?7h[?12l[?25h[?25l[?7lommon_valuation

 lau.category               lau.common_valuation      [?7h[?12l[?25h[?25l[?7ldup

 lau.common_valuation       lau.dump                  [?7h[?12l[?25h[?25l[?7lfactor

 additive_ordercategory      ommon_valuationdup            factor

 base_extendchang_rigdegre     umps gcd  

<bae_ringcoefficientsdenomnator eucliden_degreeintegral        

 cartesian_productommon_prec      derivativ exponents inverse  [?7h[?12l[?25h[?25l[?7linverse_of_unit

category      ommon_valuationdup            factorinverse_of_unit

chang_rigdegre     umps gcd  is_idempotent

coefficientsdenomnator eucliden_degreeintegral        s_monomial

ommon_prec      derivativ exponents inverse  s_nilpotent[?7h[?12l[?25h[?25l[?7ls_one

ommon_valuationdup            factorinverse_of_units_one         

degre     umps gcd  is_idempotentprie     

denomnator eucliden_degreeintegral        s_monomialunit    

derivativ exponents inverse  s_nilpotentzero     [?7h[?12l[?25h[?25l[?7llaurent_polynomial

dup            factorinverse_of_units_one         laurent_polynomial

umps gcd  is_idempotentprie     lcm     

eucliden_degreeintegral        s_monomialunit    lift_to_precision

exponents inverse  s_nilpotentzero     list   [?7h[?12l[?25h[?25l[?7lmultiplicative_order

factorinverse_of_units_one         laurent_polynomialmultiplicative_order

gcd  is_idempotentprie     lcm     n  

integral        s_monomialunit    lift_to_precisionnth_rot         

inverse  s_nilpotentzero     list   numerator[?7h[?12l[?25h[?25l[?7lnmerical_approx

inverse_of_units_one         laurent_polynomialmultiplicative_ordernmerical_approx    

is_idempotentprie     lcm     n  order

s_monomialunit    lift_to_precisionnth_rot         parent  

s_nilpotentzero     list   numeratorpow_seies[?7h[?12l[?25h[?25l[?7lmltiplicative_order

 lau.multiplicative_order   lau.numerical_approx      [?7h[?12l[?25h[?25l[?7llaurent_polynomial

 lau.laurent_polynomial     lau.multiplicative_order  [?7h[?12l[?25h[?25l[?7lis_one

 lau.is_one                 lau.laurent_polynomial    [?7h[?12l[?25h[?25l[?7lnverse_of_unit

 lau.inverse_of_unit        lau.is_one                [?7h[?12l[?25h[?25l[?7lfactor

factor         nverse_of_unitis_one            laurent_polynomial  mltiplicative_order

gcd          idepotentis_primelcmn    

ntegral   monomialis_unit          lift_t_precisionnth_root

nverse     nilpotentis_zerolist     numato   [?7h[?12l[?25h[?25l[?7ldump

dump  factor         nverse_of_unitis_one            laurent_polynomial  

dumpsgcd          idepotentis_primelcm

euclidean_degreentegral   monomialis_unit          lift_t_precision

exponentsnverse     nilpotentis_zerolist     [?7h[?12l[?25h[?25l[?7lcomon_valuation

comon_valuationdump  factor         nverse_of_unitis_one            

egreedumpsgcd          idepotentis_prime

denomintor     euclidean_degreentegral   monomialis_unit          

derivativeexponentsnverse     nilpotentis_zero[?7h[?12l[?25h[?25l[?7lategory

ategory        comon_valuationdump  factor         nverse_of_unit

chang_ringegreedumpsgcd          idepotent

coeffcientsdenomintor     euclidean_degreentegral   monomial

common_prcderivativeexponentsnverse     nilpotent[?7h[?12l[?25h[?25l[?7ladditive_order

additive_orderategory        comon_valuationdump  factor         

base_xtedchang_ringegreedumpsgcd          

base_ring   coeffcientsdenomintor     euclidean_degreentegral   

artesian_productcommon_prcderivativeexponentsnverse     [?7h[?12l[?25h[?25l[?7lO

 O             additive_orderategory        comon_valuationdump  

 V          base_xtedchang_ringegreedumps

 ab      base_ring   coeffcientsdenomintor     euclidean_degree

 add_bigoh        artesian_productcommon_prcderivativeexponents[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.pth_root()[?7h[?12l[?25h[?25l[?7lor a in range(0, 9):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lprint(a*(C.x.teichmuller().diffn()) == a*(C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents():

....:     print(lau.coefficient(t^i))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [100], in <cell line: 1>()
      1 for i in lau.exponents():
----> 2     print(lau.coefficient(t**i))

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'coefficient'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.lift_to_precision(0)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: lau.lift_to_precision(0)

  lau.O                      lau.additive_order         lau.category               lau.common_valuation       lau.dump                    

  lau.V                      lau.base_extend            lau.change_ring            lau.degree                 lau.dumps                   

  lau.abs                    lau.base_ring              lau.coefficients           lau.denominator            lau.euclidean_degree       >

  lau.add_bigoh              lau.cartesian_product      lau.common_prec            lau.derivative             lau.exponents               

 [?7h[?12l[?25h[?25l[?7lO

 lau.O                     







 <unknown> [?7h[?12l[?25h[?25l[?7ladditive_order

 lau.O                      lau.additive_order        [?7h[?12l[?25h[?25l[?7lO

 lau.O                      lau.additive_order        [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in lau.exponents():

....:     print(lau.coefficient(t^i))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7li])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([i])[?7h[?12l[?25h[?25l[?7l)[i])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents():

....:     print(lau.coefficient()[i])

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [101], in <cell line: 1>()
      1 for i in lau.exponents():
----> 2     print(lau.coefficient()[i])

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'coefficient'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents():

....:     print(lau.coefficient()[i])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(lau[i])

....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents():

....:     print(lau[i])

....: 

[?7h[?12l[?25h[?2004l1
1
1
1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents():

....:     print(lau[i])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lilau[i])[?7h[?12l[?25h[?25l[?7l,lau[i])[?7h[?12l[?25h[?25l[?7l lau[i])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(i, lau[i])

....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents():

....:     print(i, lau[i])

....: 

[?7h[?12l[?25h[?2004l-6 1
-2 1
0 1
2 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h1 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7h1 + 2*t^16 + 2*t^48 + t^64 + O(t^100)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.diffn()[?7h[?12l[?25h[?25l[?7l = om1.pth_root()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.pth_rot()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.cartier().cartier()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lint().diffn()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.inv_cartier()

[?7h[?12l[?25h[?2004l[?7h((x^18 - x^10)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.inv_cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.inv_cartier().inv_cartier()

[?7h[?12l[?25h[?2004l[?7h((x^63 - x^55 - x^39 + x^31)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lmom1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l2om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l=om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = om1.inv_cartier().inv_cartier()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpip install -U sage[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.inv_cartier().nv_cartier()[?7h[?12l[?25h[?25l[?7l = om.cartier().cartier()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.expansonat_infty()[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7losecond_patch(om)[?7h[?12l[?25h[?25l[?7lmsecond_patch(om)[?7h[?12l[?25h[?25l[?7l1second_patch(om)[?7h[?12l[?25h[?25l[?7l second_patch(om)[?7h[?12l[?25h[?25l[?7l=second_patch(om)[?7h[?12l[?25h[?25l[?7l second_patch(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = second_patch(om)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = second_patch(om)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.inv_artier().inv_cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier().cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier().cartier().inv_cartier().inv_cartier()

[?7h[?12l[?25h[?2004l[?7h((-x^36 + x^28 + x^12 - x^4)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.lift_to_precision(0)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lplau[?7h[?12l[?25h[?25l[?7lalau[?7h[?12l[?25h[?25l[?7lrlau[?7h[?12l[?25h[?25l[?7lelau[?7h[?12l[?25h[?25l[?7lnlau[?7h[?12l[?25h[?25l[?7ltlau[?7h[?12l[?25h[?25l[?7l(lau[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(lau)

[?7h[?12l[?25h[?2004l[?7hLaurent Series Ring in t over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(lau)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lparent(lau)[?7h[?12l[?25h[?25l[?7laparent(lau)[?7h[?12l[?25h[?25l[?7lrparent(lau)[?7h[?12l[?25h[?25l[?7leparent(lau)[?7h[?12l[?25h[?25l[?7lntparent(lau)[?7h[?12l[?25h[?25l[?7l(parent(lau)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: parent(parent(lau))

[?7h[?12l[?25h[?2004l[?7h<class 'sage.rings.laurent_series_ring.LaurentSeriesRing_with_category'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(parent(lau))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb(parent(lau))[?7h[?12l[?25h[?25l[?7la(parent(lau))[?7h[?12l[?25h[?25l[?7ls(parent(lau))[?7h[?12l[?25h[?25l[?7le(parent(lau))[?7h[?12l[?25h[?25l[?7l_(parent(lau))[?7h[?12l[?25h[?25l[?7lr(parent(lau))[?7h[?12l[?25h[?25l[?7li(parent(lau))[?7h[?12l[?25h[?25l[?7ln(parent(lau))[?7h[?12l[?25h[?25l[?7lg(parent(lau))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: base_ring(parent(lau))

[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.lift_to_precision(0)[?7h[?12l[?25h[?25l[?7load('ini.sag')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: load('auxilliar

 auxilliaries/        

 auxilliary_derivative





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lies/

 auxilliaries/        



 <unknown> [?7h[?12l[?25h[?25l[?7ll





[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_analytic_part.sage[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lau.lift_to_preciion(0)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lanalytic_part[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau)

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7lrent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [121], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier().cartier().inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.cartier().cartier().inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.cartier()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l = om.crtier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: lau = om1.expansion

 om1.expansion         

 om1.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 om1.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 om1.expansion         

 om1.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau = om1.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7llau = om1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.lift_to_recsion(0)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.analytic_part().integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [125], in <cell line: 1>()
----> 1 lau.analytic_part().integral()

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'analytic_part'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.analytic_part().integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lanalytic_part().integral()[?7h[?12l[?25h[?25l[?7lranalytic_part().integral()[?7h[?12l[?25h[?25l[?7leanalytic_part().integral()[?7h[?12l[?25h[?25l[?7lnanalytic_part().integral()[?7h[?12l[?25h[?25l[?7ltanalytic_part().integral()[?7h[?12l[?25h[?25l[?7l_analytic_part().integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ll).integral()[?7h[?12l[?25h[?25l[?7la).integral()[?7h[?12l[?25h[?25l[?7lu).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [126], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.aalytic_part().integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrt().integral()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.analytic_part()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [127], in <cell line: 1>()
----> 1 lau.analytic_part()

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'analytic_part'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.analytic_part()[?7h[?12l[?25h[?25l[?7lret_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau)

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7load('auxiliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004llo[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lafty/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(uxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C
.

....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9
*

....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C
.

....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9
*

....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().cartier().expansion_at_infty(prec = 100)

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7h1 + 2*t^16 + 2*t^48 + t^64 + O(t^100)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h((x^13 - x^12 - x^11 - x^10 - x^9 + x^8 - x^5 + x^4 - x^3 - x^2 + x - 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7laom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7luom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_anlytic_part(lau)[?7h[?12l[?25h[?25l[?7lent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau)

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lintegral()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7load('auxiliaries/laurent_aalytic_part.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lauxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(uxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C
.

....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9
*

....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(



)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

(

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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(



)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10 - 
C

.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C.x^
9

*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10 -


C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C.x
^

9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10 
-

 C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C.
x

^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10


- C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C
.

x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7laom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7luom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7llau = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau

[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.analytic_part()[?7h[?12l[?25h[?25l[?7litegral()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lintegral()[?7h[?12l[?25h[?25l[?7lsage: lau.integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 lau.integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR == gg.pth_root().diffn()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: F

[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR == gg.pth_root().diffn()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lL[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: Rt.<t> = LaurentSeries

 LaurentSeries    

 LaurentSeriesRing





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 LaurentSeries    



 <unknown> [?7h[?12l[?25h[?25l[?7lRing

 LaurentSeries    

 LaurentSeriesRing[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rt.<t> = LaurentSeriesRing(F)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: t.integral()

[?7h[?12l[?25h[?2004l[?7h2*t^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7llau.integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau

[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt.integral()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: t^(-8).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 t**(-Integer(8)).integral()

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'integral'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-8).integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (t^(-8)).integral()

[?7h[?12l[?25h[?2004l[?7h2*t^-7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-8)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)).integral()[?7h[?12l[?25h[?25l[?7l6)).integral()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (t^(-6)).integral()

[?7h[?12l[?25h[?2004l[?7ht^-5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lau

[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)).integral()[?7h[?12l[?25h[?25l[?7l4)).integral()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (t^(-4)).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 (t**(-Integer(4))).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-4)).integral()[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7l(t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7lt.integral()[?7h[?12l[?25h[?25l[?7lRt.<> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7llau.integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.integral()[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lt.inegral()[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7l(t^(-8)).integral()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7l(t^(-4)).integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h((x^6 + x^3 - x^2 - 1)/(x^6*y + x^4*y + x^2*y + y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7h1 + t^4 + t^6 + 2*t^8 + t^10 + 2*t^20 + t^22 + 2*t^26 + 2*t^28 + t^30 + 2*t^34 + t^36 + t^38 + t^40 + t^42 + 2*t^46 + t^52 + t^54 + 2*t^56 + t^58 + t^60 + 2*t^64 + t^66 + t^68 + 2*t^72 + t^74 + t^76 + 2*t^80 + t^82 + t^84 + 2*t^88 + t^90 + t^92 + 2*t^96 + t^98 + O(t^100)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.genus()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: g = C.genus()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^(g+1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lxpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: v.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^2 - u + u^3[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lov^(-4)*[?7h[?12l[?25h[?25l[?7lmv^(-4)*[?7h[?12l[?25h[?25l[?7l v^(-4)*[?7h[?12l[?25h[?25l[?7l=v^(-4)*[?7h[?12l[?25h[?25l[?7l v^(-4)*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = v^(-4)*v.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = v^(-4)*v.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-4 + t^4 + O(t^6)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h(x^3/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + O(t^8)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + O(t^8)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h(x^6/(x^4*y + x^2*y + y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h(x^3/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = v^(-4)*v.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier()

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7lsage: om.cartier()

[?7h[?12l[?25h[?2004l[?7h((x^11 + x^9 - x^7 - x^4 - x)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7h1 + t^4 + t^6 + 2*t^8 + t^10 + 2*t^20 + t^22 + 2*t^26 + 2*t^28 + t^30 + 2*t^34 + t^36 + t^38 + t^40 + t^42 + 2*t^46 + t^52 + t^54 + 2*t^56 + t^58 + t^60 + 2*t^64 + t^66 + t^68 + 2*t^72 + t^74 + t^76 + 2*t^80 + t^82 + t^84 + 2*t^88 + t^90 + t^92 + 2*t^96 + t^98 + O(t^100)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7load('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(it.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C
.

....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9
*

....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C
.

....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9
*

....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().cartier().expansion_at_infty(prec = 100)

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + O(t^-8)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50)

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l= g.diffn()

 

 [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^
1

....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y -

....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om == ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^
1

....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y -

....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om == ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^
1

....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y -
 

....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()

 

 [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lau[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty(prec = 30)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau = om.cartier().expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: laux

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 laux

NameError: name 'laux' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaux[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + t^6 + 2*t^10 + t^14 + t^16 + 2*t^18 + 2*t^22 + O(t^24)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7lent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + t^6 + 2*t^10 + t^14 + t^16 + 2*t^18 + 2*t^22 + O(t^24)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7lent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau)

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lsage: Rt.<t> = LaurentSeriesRing(F)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C
.

....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9
*

....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lt^(-4)).integral()

 

 [?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7lsage: (t^(-6)).integral()

[?7h[?12l[?25h[?2004l[?7ht^-5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)).integral()[?7h[?12l[?25h[?25l[?7l2)).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (t^(-2)).integral()

[?7h[?12l[?25h[?2004l[?7h2*t^-1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-2)).integral()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lR.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7llaurent_anlytic_part(lau)[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau)

[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lintegral()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).int()

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'int'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7lg()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7ll()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7legral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7legral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-2)).integral()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2)).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (t^(-2) + t^(-6)).integral()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 (t**(-Integer(2)) + t**(-Integer(6))).integral()

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
   1652 
   1653         if n < 0:
-> 1654             v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
   1655         else:
   1656             v = []

File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-2) + t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()) + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l(). + t^(-6).integral()[?7h[?12l[?25h[?25l[?7li + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lin + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lint + t^(-6).integral()[?7h[?12l[?25h[?25l[?7le + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lg + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lr + t^(-6).integral()[?7h[?12l[?25h[?25l[?7la + t^(-6).integral()[?7h[?12l[?25h[?25l[?7ll + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l( + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l() + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-6).integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (t^(-2)).integral() + (t^(-6)).integral()

[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^-1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(uxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(t^(-2)).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7laurent_anaytic_part(lau).itegral()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llytic_part[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: laurent_integral(laurent_analytic_part(lau))

[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^-1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_integral(laurent_analytic_part(lau))[?7h[?12l[?25h[?25l[?7load('auxilliaries/laurent_nalytic_part.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
OSError                                   Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:21, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach)
    242         break
    243 else:
--> 244     raise IOError('did not find file %r to load or attach' % filename)
    246 ext = os.path.splitext(fpath)[1].lower()
    247 if ext == '.py':

OSError: did not find file 'sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage' to load or attach
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: Rx

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in lau.exponents():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.genus()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g = x^3 - x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^3 - x[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x = C.x/C.y)

[?7h[?12l[?25h[?2004lsage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
  """
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
  """
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 g(x = C.x/C.y)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:332, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__call__()
    330             nmod_poly_compose(&t.x, &self.x, &y.x)
    331             return t
--> 332     return Polynomial.__call__(self, *x, **kwds)
    333 
    334 @coerce_binop

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:870, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    868 # This can save lots of coercions when the common parent is the
    869 # polynomial's base ring (e.g., for evaluations at integers).
--> 870 cst, aa = coercion_model.canonical_coercion(cst, a)
    871 # Use fast multiplication actions like matrix × scalar.
    872 # If there is no action, replace a by an element of the

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1391         self._record_exception()
   1392 
-> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp))
   1394 
   1395 

TypeError: no common canonical parent for objects with parents: 'Finite Field of size 3' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1

....: ....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10
*

....: C.y -

....: ....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1

....: ....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10
*

....: C.y -

....: ....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l  Input In [8]
    ((C.x**Integer(28) - C.x**Integer(26) + C.x**Integer(25) - C.x**Integer(24) + C.x**Integer(23) - C.x**Integer(22) - C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(15) - C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) - C.x**Integer(1)
      ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om == ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^
1

....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y -
 

....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l (C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y)*C.dx[?7h[?12l[?25h[?25l[?7l

  %%!                                          AbelianGroupWithValues                       AdditiveAbelianGroupWrapperElement            

....: .x^9*  AA                                           AbelianVariety                               AdditiveMagmas                                

  AbelianGroup                                 AdditiveAbelianGroup                         AffineCryptosystem                           >

  AbelianGroupMorphism                         AdditiveAbelianGroupWrapper                  AffineGroup                                   

 [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx



[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lom = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmposition

 decomposition               decomposition_g0_pth_power  decomposition_omega8_hpdh  

                    decomposition_g0_g8         decomposition_omega0_hpdh                              

 decomposition_g0_p2th_power decomposition_omega0_omega8                            



 [?7h[?12l[?25h[?25l[?7l

 decomposition              





 <unknown> [?7h[?12l[?25h[?25l[?7l_g0_g8

 decomposition              

 decomposition_g0_g8        [?7h[?12l[?25h[?25l[?7lp2th_power



 decomposition_g0_g8        

 decomposition_g0_p2th_power[?7h[?12l[?25h[?25l[?7lomega0_omega8





 decomposition_g0_p2th_power decomposition_omega0_omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lhpdh



 decomposition_omega0_hpdh  

 decomposition_omega0_omega8[?7h[?12l[?25h[?25l[?7lg0_pthpower

 decomposition_g0_pth_power 

 decomposition_omega0_hpdh  [?7h[?12l[?25h[?25l[?7lomega8hpdh

 decomposition_g0_pth_power  decomposition_omega8_hpdh  [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)

File <string>:32, in decomposition_omega8_hpdh(omega, prec)

NameError: name 'laurent_analytic_part' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3-x)^3 +x^3 - x,2)

 

 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lom = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)

 

 [?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004l[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()

 

 [?7h[?12l[?25h[?25l[?7lexpansion_at_ifty(prec = 50)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50)

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic t^-6 + t^-2
omega_analytic (x^30 + x^10*y^4)/y^6
omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx
dh 0 dx
[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic t^-6 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^30 + x^10*y^4)/y^6 (x^27 + x^25 + x^17 + x^9)/(x^24 + 2) (x^3/y) dx
omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx
dh 0 dx
[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic t^-6 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^30 + x^10*y^4)/y^6 (x^27 + x^25 + x^17 + x^9)/(x^24 + 2) (x^3/y) dx
omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx
dh 0 dx
omega8.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + O(t^-8)
[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 50)

 

 [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50)

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7luom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lrom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7leom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lnom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7ltom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l_om.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lnom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7llom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lyom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7ltom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7liom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lcom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l_om.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lpom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lrom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7ltom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l(om.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(om.expansion_at_infty(prec = 50))

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(om.expansion_at_infty(prec = 50))[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l-auxf.t.teichmuller()diffn()

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + O(t^8)
[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
 ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l= C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x = C.x/C.y)[?7h[?12l[?25h[?25l[?7l =x^3 - x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7lsage: g = C.genus()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l= C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^(g+1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: v.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldexpansion_at_infty()[?7h[?12l[?25h[?25l[?7liexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lnexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l(expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h1 + O(t^10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + O(t^-8)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + O(t^8)
[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
 ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
 ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category()
    838 try:
--> 839     return self.__cached_methods[name]
    840 except KeyError:

KeyError: 'integer_ring'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
    705 try:
--> 706     x, y = resolve_fractions(x0, y0)
    707 except (AttributeError, TypeError):

File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
    682 def resolve_fractions(x, y):
--> 683     xn = x.numerator()
    684     xd = x.denominator()

File /ext/sage/9.7/src/sage/categories/complete_discrete_valuation.py:281, in CompleteDiscreteValuationFields.ElementMethods.numerator(self)
    252 """
    253 Return the numerator of this element, normalized in such a
    254 way that `x = x.numerator() / x.denominator()` always holds
   (...)
    279     7^5 + O(7^10)
    280 """
--> 281 R = self.parent().integer_ring()
    282 return R(self * self.denominator())

File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
    832 """
--> 833 return self.getattr_from_category(name)
    834 

File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
    847 
--> 848             attr = getattr_from_other_class(self, cls, name)
    849             self.__cached_methods[name] = attr

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
    355     dummy_error_message.name = name
--> 356     raise AttributeError(dummy_error_message)
    357 cdef PyObject* attr = instance_getattr(cls, name)

AttributeError: 'PolynomialRing_dense_mod_p_with_category' object has no attribute '_cached_repr'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)

File <string>:34, in decomposition_omega8_hpdh(omega, prec)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
    706     x, y = resolve_fractions(x0, y0)
    707 except (AttributeError, TypeError):
--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))
    710 try:
    711     return self._element_class(self, x, y, coerce=coerce)

TypeError: cannot convert t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2/1 to an element of Fraction Field of Univariate Polynomial Ring in T over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
 ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)

File <string>:39, in decomposition_omega8_hpdh(omega, prec)

AttributeError: 'superelliptic_function' object has no attribute 'expanstion_at_infty'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 1 + t^2 + t^12 + 2*t^14 + 2*t^16 + t^18 + 2*t^28 + 2*t^30 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
 ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [65], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)

File <string>:39, in decomposition_omega8_hpdh(omega, prec)

TypeError: superelliptic_function.diffn() got an unexpected keyword argument 'prec'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 1 + t^2 + t^12 + 2*t^14 + 2*t^16 + t^18 + 2*t^28 + 2*t^30 + O(t^32) 
 1 + 2*t^16 + 2*t^48 + O(t^50) 
 t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
 ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloal[?7h[?12l[?25h[?25l[?7lsage: loal

















 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 













 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 









 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y.exansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer()

[?7h[?12l[?25h[?2004l[?7h(x^4/(x^8 + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer()

[?7h[?12l[?25h[?2004l[?7h(x^4/(x^8 + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200)

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^199)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:219: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^199)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + O(t^18)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:219: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = suerelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.x.exansion_at_infty()[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.x.exansion_at_infty()[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht + O(t^201)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht + O(t^201)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht + O(t^221)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.uniformizer().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()^.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^219)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l320)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 320)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + t^255 + 2*t^271 + O(t^319)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1)).expansion_at_infty(prec = 320)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l10)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 1000)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + t^255 + 2*t^271 + 2*t^319 + 2*t^431 + 2*t^447 + 2*t^463 + 2*t^479 + t^559 + t^575 + t^591 + t^623 + t^751 + 2*t^975 + O(t^999)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 20)

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + O(t^18)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l30)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l10)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer()

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7h1/x^5*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?7ht + O(t^221)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = C.uniformizer()

[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.uniformizer()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^(-1).expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l10)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (a^(-1)).expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + O(t^99)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.uniformizer()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a^(-1)

[?7h[?12l[?25h[?2004l[?7h(x^4/(x^8 + 2))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C.y^2

[?7h[?12l[?25h[?2004l[?7hx^9 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7l.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lsage: Rt.<t> = LaurentSeriesRing(F)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly^2[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + O(t^11)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + 2*t^23 + 2*t^55 + 2*t^71 + t^87 + O(t^91)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^(-1)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lt2integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l()).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l() + t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xx = t^(-2) + t^(14) + 2*t^(30)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: yy = t^(-9) + 2*t^7 + 2*t^23

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l8)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xx^4*yy/(xx^8 - 1)

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-1)[?7h[?12l[?25h[?25l[?7l = C.uniformizer()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x - a^(-2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx - a^(-2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.x - a^(-2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x - a^(-2)).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^14 + O(t^34)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x - a^(-2)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x - a^(-2)).expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7h2*t^14 + 2*t^62 + t^110 + O(t^114)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: xx^8 - 1

[?7h[?12l[?25h[?2004l[?7ht^-16 + 1 + 2*t^16 + 2*t^48 + t^64 + t^80 + t^112 + t^144 + 2*t^160 + 2*t^176 + 2*t^208 + t^224 + t^240
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^8 - 1[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy/xx^5

[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lt.<t> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rt.<t> = LaurentSeriesRing(F, prec = 100)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [116], in <cell line: 1>()
----> 1 Rt = LaurentSeriesRing(F, prec = Integer(100), names=('t',)); (t,) = Rt._first_ngens(1)

File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
    318 """
    319 if cls.classcall is not None:
--> 320     return cls.classcall(cls, *args, **kwds)
    321 else:
    322     # Fast version of type.__call__(cls, *args, **kwds)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:201, in LaurentSeriesRing.__classcall__(cls, *args, **kwds)
    199     power_series = args[0]
    200 else:
--> 201     power_series = PowerSeriesRing(*args, **kwds)
    203 return UniqueRepresentation.__classcall__(cls, power_series)

TypeError: PowerSeriesRing() got an unexpected keyword argument 'prec'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F, prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldprec = 10)[?7h[?12l[?25h[?25l[?7leprec = 10)[?7h[?12l[?25h[?25l[?7lfprec = 10)[?7h[?12l[?25h[?25l[?7laprec = 10)[?7h[?12l[?25h[?25l[?7luprec = 10)[?7h[?12l[?25h[?25l[?7llprec = 10)[?7h[?12l[?25h[?25l[?7ltprec = 10)[?7h[?12l[?25h[?25l[?7l_prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li = 10)[?7h[?12l[?25h[?25l[?7ls = 10)[?7h[?12l[?25h[?25l[?7li = 10)[?7h[?12l[?25h[?25l[?7lo = 10)[?7h[?12l[?25h[?25l[?7ln = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rt.<t> = LaurentSeriesRing(F, default_precision = 100)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [117], in <cell line: 1>()
----> 1 Rt = LaurentSeriesRing(F, default_precision = Integer(100), names=('t',)); (t,) = Rt._first_ngens(1)

File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
    318 """
    319 if cls.classcall is not None:
--> 320     return cls.classcall(cls, *args, **kwds)
    321 else:
    322     # Fast version of type.__call__(cls, *args, **kwds)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:201, in LaurentSeriesRing.__classcall__(cls, *args, **kwds)
    199     power_series = args[0]
    200 else:
--> 201     power_series = PowerSeriesRing(*args, **kwds)
    203 return UniqueRepresentation.__classcall__(cls, power_series)

TypeError: PowerSeriesRing() got an unexpected keyword argument 'default_precision'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F, default_precision = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7lsage: Rt.<t> = LaurentSeriesRing(F, default_prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F, default_prec = 100)[?7h[?12l[?25h[?25l[?7lision = 100)[?7h[?12l[?25h[?25l[?7lprec = 100)[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7lxx^8 - 1[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l(C.x - ^(-2)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7lyy = t^(-9) +2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7lxx2t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lsage: xx = t^(-2) + t^(14) + 2*t^(30)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7lsage: yy = t^(-9) + 2*t^7 + 2*t^23

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx^5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: yy/xx^5

[?7h[?12l[?25h[?2004l[?7ht + t^49 + t^65 + 2*t^97 + O(t^101)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^8- 1[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: xx^5/yy

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^47 + 2*t^63 + 2*t^95 + O(t^99)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^5/yy[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4*/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xx^4*yy/(xx^8 - 1)

[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + 2*t^31 + t^47 + 2*t^79 + 2*t^95 + O(t^99)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (xx^8 - 1)/(xx^4 * yy)

[?7h[?12l[?25h[?2004l[?7ht + t^17 + 2*t^33 + 2*t^49 + t^81 + t^97 + O(t^101)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C.y^2

[?7h[?12l[?25h[?2004l[?7hx^9 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yy^2 - xx^9 + xx

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + t^30 + t^46 + 2*t^126 + t^270
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C.y^2

[?7h[?12l[?25h[?2004l[?7hx^9 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - xx^9 + xx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l&[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^9 +2*xx)

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + t^30 + t^46 + 2*t^126 + t^270
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^9 +2*xx)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: yy

[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + 2*t^23
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2 - (xx^9 +2*xx)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: yy^2

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-2 + 2*t^14 + 2*t^30 + t^46
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx^9 + 2*xx

[?7h[?12l[?25h[?2004l[?7ht^-18 + 2*t^-2 + 2*t^14 + t^30 + t^126 + 2*t^270
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7l()x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7l^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^9 + 2*xx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l =t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expanstion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [135], in <cell line: 1>()
----> 1 yy = C.y.expanstion_at_infty(prec = Integer(100))

AttributeError: 'superelliptic_function' object has no attribute 'expanstion_at_infty'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expanstion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - (xx^9 +2*xx)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 - xx)

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + t^6 + t^10 + 2*t^14 + t^18 + t^34 + 2*t^38 + t^42 + t^46 + 2*t^50 + t^54 + O(t^94)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 - xx)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: yy

[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t + 2*t^5 + 2*t^9 + t^13 + 2*t^17 + 2*t^33 + t^37 + 2*t^41 + 2*t^45 + t^49 + 2*t^53 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(xx^8 - 1)/(xx^4 * yy)[?7h[?12l[?25h[?25l[?7lC.x - a^(-2)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly*v^2 - C.y^2*v).cordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.genus()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*v^2 - C.y^2*v).coordinates()[?7h[?12l[?25h[?25l[?7l*v^2 - C.y^2*v).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y^2).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + 1 + 2*t^2 + t^4 + 2*t^6 + O(t^14)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l= C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l= C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2- (xx^3 - xx)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - (xx^3 - xx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 - xx + 1)

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 1 + 2*t^4 + 2*t^6 + 2*t^8 + 2*t^10 + 2*t^12 + 2*t^14 + t^28 + t^30 + t^32 + 2*t^40 + 2*t^42 + 2*t^44 + 2*t^46 + 2*t^48 + 2*t^50 + t^52 + t^54 + t^56 + t^82 + t^84 + t^86 + 2*t^88 + 2*t^90 + 2*t^92 + O(t^94)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2 - (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l =C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: yy

[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t + 2*t^5 + 2*t^9 + t^13 + 2*t^17 + 2*t^33 + t^37 + 2*t^41 + 2*t^45 + t^49 + 2*t^53 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: 1/xx

[?7h[?12l[?25h[?2004l[?7ht^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^102)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbase_ring(parent(lau))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b = F(2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = F(2)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lot([?7h[?12l[?25h[?25l[?7lrot([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.nth_root(2)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [152], in <cell line: 1>()
----> 1 b.nth_root(Integer(2))

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:1572, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.nth_root()
   1570         else:
   1571             return sign[0] * K(R.teichmuller(modp) * (plog // n).exp())
-> 1572     return self._nth_root_common(n, all, algorithm, cunningham)
   1573 
   1574 def _nth_root_naive(self, n):

File /ext/sage/9.7/src/sage/rings/finite_rings/element_base.pyx:74, in sage.rings.finite_rings.element_base.FiniteRingElement._nth_root_common()
     72 if n == 0:
     73     if all: return []
---> 74     else: raise ValueError("no nth root")
     75 gcd, alpha, beta = n.xgcd(q-1) # gcd = alpha*n + beta*(q-1), so 1/n = alpha/gcd (mod q-1)
     76 if gcd == 1:

ValueError: no nth root
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.nth_root(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b.nth_root(3)

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:219: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004lww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + O(t^100)
[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004la, b, delta, M, R 2 1 1 2 3
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220)
[?7ht + O(t^221)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:219: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004lww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + O(t^100)
[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:219: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004la, b, delta, M, R 1 1 1 2 3
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220)
[?7ht + O(t^221)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.uniformizer().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()^.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004la, b, delta, M, R 1 1 1 2 3
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220)
[?7ht^-1 + O(t^219)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l(x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l(x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lom = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + 1 + t^2 + t^12 + 2*t^16 + t^18 + 2*t^28 + O(t^32) 
 1 + t^16 + t^48 + O(t^50) 
 t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^12 + 2*t^18 + t^30 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^12 + 2*t^18 + t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 - x^75 - x^74 - x^69 - x^66 + x^53 - x^45 + x^29 - x^21)/(x^72*y - y)) dx
omega8 ((-x^77 - x^76 + x^75 - x^74 + x^73 + x^72 - x^69 - x^67 + x^65 - x^61 + x^57 + x^56 - x^53 - x^51 + x^49 - x^48 - x^45 + x^43 + x^41 - x^37 + x^33 + x^32 - x^29 - x^27 + x^25 - x^24 - x^21 + x^19 + x^17 + x^13 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() 2*t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^16 + 2*t^18 + t^20 + 2*t^22 + 2*t^30 + 2*t^40 + t^46 + O(t^48)
[?7h(((-x^77 - x^76 + x^75 - x^74 + x^73 + x^72 - x^69 - x^67 + x^65 - x^61 + x^57 + x^56 - x^53 - x^51 + x^49 - x^48 - x^45 + x^43 + x^41 - x^37 + x^33 + x^32 - x^29 - x^27 + x^25 - x^24 - x^21 + x^19 + x^17 + x^13 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
 ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004l[?7ht + O(t^221)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.uniformizer().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()^.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec= 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l0).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004l[?7ht^-1 + O(t^219)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 50)

 

 [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50)

[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + O(t^32)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7liexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lnexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l(expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().diffn().expansion_at_infty(prec = 220)

[?7h[?12l[?25h[?2004l[?7h1 + O(t^220)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().diffn().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - )^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) 
 1 + O(t^50) 
 t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
[?7h(((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx,
 ((x^32 + 2*x^30 + 2*x^24 + 2*x^14 + 2*x^8 + 1)/(x^34 + x^26 + x^18))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lodecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lmdecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l8decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l,decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lAdecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l=decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om8, A = decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) 
 1 + O(t^50) 
 t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom8, A = decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l= (C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^
1

0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y -
 

C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y)*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. =[?7h[?12l[?25h[?25l[?7lca ==[?7h[?12l[?25h[?25l[?7lr =[?7h[?12l[?25h[?25l[?7lt =[?7h[?12l[?25h[?25l[?7le =[?7h[?12l[?25h[?25l[?7l =[?7h[?12l[?25h[?25l[?7li =[?7h[?12l[?25h[?25l[?7le =[?7h[?12l[?25h[?25l[?7lr =[?7h[?12l[?25h[?25l[?7l( =[?7h[?12l[?25h[?25l[?7l() =[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() == om8.cartier() + A.diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier() == om8.cartier() + A.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l8, A = decomposition_omga8_hpdh(om)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7lsage: om8.is_regu;

  %%!                                          AbelianGroupMorphism                         AdditiveAbelianGroupWrapper                   

  A                                            AbelianGroupWithValues                       AdditiveAbelianGroupWrapperElement            

  AA                                           AbelianVariety                               AdditiveMagmas                               >

  AbelianGroup                                 AdditiveAbelianGroup                         AffineCryptosystem                            

 [?7h[?12l[?25h[?25l[?7l







[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lar_on_U

 om8.is_regular_on_U0    

 om8.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7l0

 om8.is_regular_on_U0    



 <unknown> [?7h[?12l[?25h[?25l[?7linfty

 om8.is_regular_on_U0    

 om8.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om8.is_regular_on_Uinfty()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gigit add auxsuperelliptic_arbitrary_field.ipynb age/superelliptic_drw/superelliptic_drw_auxilliaries.sage 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ aigit add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit - mm "naprawiony problem z uniformizatorem w superelliptic; decomposition_omega8_hpdh dziala"
[master 995d5f0] naprawiony problem z uniformizatorem w superelliptic; decomposition_omega8_hpdh dziala
 7 files changed, 3618 insertions(+), 35 deletions(-)
 create mode 100644 sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 22, done.
Counting objects:   4% (1/22)
Counting objects:   9% (2/22)
Counting objects:  13% (3/22)
Counting objects:  18% (4/22)
Counting objects:  22% (5/22)
Counting objects:  27% (6/22)
Counting objects:  31% (7/22)
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Counting objects:  50% (11/22)
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Counting objects:  77% (17/22)
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Counting objects:  86% (19/22)
Counting objects:  90% (20/22)
Counting objects:  95% (21/22)
Counting objects: 100% (22/22)
Counting objects: 100% (22/22), done.
Delta compression using up to 4 threads
Compressing objects:   8% (1/12)
Compressing objects:  16% (2/12)
Compressing objects:  25% (3/12)
Compressing objects:  33% (4/12)
Compressing objects:  41% (5/12)
Compressing objects:  50% (6/12)
Compressing objects:  58% (7/12)
Compressing objects:  66% (8/12)
Compressing objects:  75% (9/12)
Compressing objects:  83% (10/12)
Compressing objects:  91% (11/12)
Compressing objects: 100% (12/12)
Compressing objects: 100% (12/12), done.
Writing objects:   8% (1/12)
Writing objects:  16% (2/12)
Writing objects:  25% (3/12)
Writing objects:  33% (4/12)
Writing objects:  41% (5/12)
Writing objects:  50% (6/12)
Writing objects:  58% (7/12)
Writing objects:  66% (8/12)
Writing objects:  75% (9/12)
Writing objects:  83% (10/12)
Writing objects:  91% (11/12)
Writing objects: 100% (12/12)
Writing objects: 100% (12/12), 40.37 KiB | 359.00 KiB/s, done.
Total 12 (delta 10), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   42ccc4d..995d5f0  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l<string>:218: DeprecationWarning: invalid escape sequence '\s'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: load('super

 super                          superelliptic_cech             superelliptic_drw_form         superelliptic_regular_drw_form supersingular_D               

 superelliptic                  superelliptic_drw/             superelliptic_form             superelliptic_regular_form     supersingular_j               

 superelliptic/                 superelliptic_drw_cech         superelliptic_function         superelliptic_witt                                           



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 super                         





 <unknown> [?7h[?12l[?25h[?25l[?7lelliptic

 super                         

 superelliptic                 [?7h[?12l[?25h[?25l[?7l/



 superelliptic                 

 superelliptic/                [?7h[?12l[?25h[?25l[?7lt







[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsts/[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty.sage[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic/tests/expansion_at_infty.sage')

[?7h[?12l[?25h[?2004lTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lload('superelliptic/tests/expansion_at_infty.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('superelliptic/tests/expansion_at_infty.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic/tests/expansion_at_infty.sage')

[?7h[?12l[?25h[?2004lTrue
True True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om)

[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
[?7h(((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx,
 ((x^32 + 2*x^30 + 2*x^24 + 2*x^14 + 2*x^8 + 1)/(x^34 + x^26 + x^18))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic/tests/expansion_at_infty.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic/tests/expansion_at_infty.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic/tests/expansion_at_infty.sage')

 super                          superelliptic_cech             superelliptic_drw_form         superelliptic_regular_drw_form supersingular_D               

 superelliptic                  superelliptic_drw/             superelliptic_form             superelliptic_regular_form     supersingular_j               

 superelliptic/                 superelliptic_drw_cech         superelliptic_function         superelliptic_witt                                           



 [?7h[?12l[?25h[?25l[?7l

 super                         





 <unknown> [?7h[?12l[?25h[?25l[?7lelliptic_cech

 super                          superelliptic_cech            [?7h[?12l[?25h[?25l[?7ldrw/

 superelliptic_cech            

 superelliptic_drw/            [?7h[?12l[?25h[?25l[?7lt







[?7h[?12l[?25h[?25l[?7lests/[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7luxilliary_decompositions_test.sage[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/tests/auxilliary_decompositions_test.sage')

[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
True
True True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/tests/auxilliary_decompositions_test.sage')[?7h[?12l[?25h[?25l[?7load('superelliptic_drw/tests/auxilliary_decompositions_test.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/tests/auxilliary_decompositions_test.sage')

[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
True
True True
True True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/tests/auxilliary_decompositions_test.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/tests/auxilliary_decompositions_test.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:103, in coordinates(self, basis)

File <string>:85, in div_by_p(self)

NameError: name 'decomposition_g8_p2th_power' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l^Csage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
  """
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
  """
---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File <string>:235, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    418      for e, val in self.dict().iteritems() if not e[ind]}
--> 419 v = [B(w)]  # coefficients that don't involve var
    420 z = var

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    468     x = x.truncate()
--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
    128         pass
--> 129 Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
    130 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:157, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
    156 for deg, coef in x.iteritems():
--> 157     celement_pow(monomial, gen, deg, NULL, (<Polynomial_template>self)._cparent)
    158     celement_mul(monomial, &(<Polynomial_template>self.__class__(parent, coef)).x, monomial, (<Polynomial_template>self)._cparent)

File /ext/sage/9.7/src/sage/libs/flint/nmod_poly_linkage.pxi:547, in sage.rings.polynomial.polynomial_zmod_flint.celement_pow()
    546 else:
--> 547     sig_on()
    548     nmod_poly_pow(res, x, e)

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:53, in crystalline_cohomology_basis(self, prec)

File <string>:25, in de_rham_witt_lift(cech_class, prec)

File <string>:15, in de_rham_witt_lift_form8(omega)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lBC.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:52, in crystalline_cohomology_basis(self, prec)

File <string>:98, in de_rham_basis(self)

File <string>:80, in basis_de_rham_degrees(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File <string>:257, in reduction_form(C, g)

File <string>:236, in reduction(C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2321, in sage.rings.polynomial.polynomial_element.Polynomial.__truediv__()
   2319 # Same parents => bypass coercion
   2320 if have_same_parent(left, right):
-> 2321     return (<Element>left)._div_(right)
   2322 
   2323 # Try division of polynomial by a scalar

File /ext/sage/9.7/src/sage/structure/element.pyx:2739, in sage.structure.element.RingElement._div_()
   2737     except AttributeError:
   2738         raise bin_op_exception('/', self, other)
-> 2739     return frac(self, other)
   2740 
   2741 def __divmod__(self, other):

File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__()
    897         return mor._call_(x)
    898     else:
--> 899         return mor._call_with_args(x, args, kwds)
    900 
    901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {}))

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:173, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
    171 else:
    172     if len(kwds) == 0:
--> 173         return C._element_constructor(x, *args)
    174     else:
    175         return C._element_constructor(x, *args, **kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field.py:648, in FractionField_generic._element_constructor_(self, x, y, coerce)
    646     x, y = x.numerator() * y.denominator(), y.numerator() * x.denominator()
    647 try:
--> 648     return self._element_class(self, x, y, coerce=coerce)
    649 except (TypeError, ValueError):
    650     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1167, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
   1165     1/2/x
   1166 """
-> 1167 FractionFieldElement.__init__(self, parent, numerator, denominator,
   1168         coerce, reduce)
   1169 if not reduce:

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:121, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    119 if reduce and parent.is_exact():
    120     try:
--> 121         self.reduce()
    122     except ArithmeticError:
    123         pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
   1237 if self._is_reduced:
   1238     return
-> 1239 super(self.__class__, self).reduce()
   1240 self.normalize_leading_coefficients()
   1241 

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    162     return codomain.coerce(nnum/nden)
    163 
--> 164 cpdef reduce(self):
    165     """
    166     Reduce this fraction.

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:198, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    196 try:
    197     g = self.__numerator.gcd(self.__denominator)
--> 198     if not g.is_unit():
    199         self.__numerator //= g
    200         self.__denominator //= g

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element_generic.py:1021, in Polynomial_generic_domain.is_unit(self)
   1019 if self.degree() > 0:
   1020     return False
-> 1021 return self[0].is_unit()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lBC.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:103, in coordinates(self, basis)

File <string>:85, in div_by_p(self)

File <string>:52, in decomposition_g8_p2th_power(fct)

NameError: name 'decomposition_g8_pth_power' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
---------------------------------------------------------------------------
ArithmeticError                           Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:103, in coordinates(self, basis)

File <string>:85, in div_by_p(self)

File <string>:67, in decomposition_g8_p2th_power(fct)

File <string>:60, in decomposition_g8_pth_power(fct, prec)

File <string>:14, in __init__(self, C, g)

File <string>:228, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    986 try:
    987     if '/' in element:
--> 988         element = sage_eval(element,d)
    989     else:
    990         element = element.replace("^","**")

File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
    196     return locals['_sage_eval_returnval_']
    197 else:
--> 198     return eval(source, sage.all.__dict__, locals)

File <string>:1, in <module>

File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
    164 elif hasattr(x, 'O'):
    165     return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))

ArithmeticError: O(y^53) not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
decomposition_omega8_hpdh ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
decomposition_g8_p2th_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
decomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
---------------------------------------------------------------------------
ArithmeticError                           Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:103, in coordinates(self, basis)

File <string>:85, in div_by_p(self)

File <string>:70, in decomposition_g8_p2th_power(fct)

File <string>:62, in decomposition_g8_pth_power(fct, prec)

File <string>:14, in __init__(self, C, g)

File <string>:228, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    986 try:
    987     if '/' in element:
--> 988         element = sage_eval(element,d)
    989     else:
    990         element = element.replace("^","**")

File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
    196     return locals['_sage_eval_returnval_']
    197 else:
--> 198     return eval(source, sage.all.__dict__, locals)

File <string>:1, in <module>

File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
    164 elif hasattr(x, 'O'):
    165     return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))

ArithmeticError: O(y^53) not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in lau.exponents():[?7h[?12l[?25h[?25l[?7lf.pth_root()[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 
+

....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
 

....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C.
x

....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7l= [?7h[?12l[?25h[?25l[?7l((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 
+

 2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
x

^47 + C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + 1)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y

 [?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 
+

....:  2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
x

....: ^47 + C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + 1)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 ff = ((Integer(2)*C.x**Integer(87) + Integer(2)*C.x**Integer(84) + C.x**Integer(83) + C.x**Integer(82) + C.x**Integer(81) + C.x**Integer(80) + Integer(2)*C.x**Integer(78) + Integer(2)*C.x**Integer(77) + C.x**Integer(76) + Integer(2)*C.x**Integer(75) + Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(72) + Integer(2)*C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(68) + Integer(2)*C.x**Integer(67) + C.x**Integer(63) + C.x**Integer(60) + Integer(2)*C.x**Integer(59) + Integer(2)*C.x**Integer(58) + Integer(2)*C.x**Integer(57) + Integer(2)*C.x**Integer(56) + C.x**Integer(54) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(51) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(48) + C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + C.x**Integer(43) + C.x**Integer(42) + Integer(2)*C.x**Integer(24) + Integer(1))/(C.x**Integer(93) + C.x**Integer(85) + C.x**Integer(77) + Integer(2)*C.x**Integer(69) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(53)))*C.y

File <string>:38, in __add__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 + 2*C
.

....: x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.x^47 
+

....:  C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(



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)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^7 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 + 2*
C

.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.x^47


+ C.x^46 + C.x^4 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^7 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7lf((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^7 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 + 2
*

C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.x^4
7

 + C.x^46 + C.x^4 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^7 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7l ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^7 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 + 
2

*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.x^
4

7 + C.x^46 + C.x^4 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^7 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7l=((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^7 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 +


2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.x
^

47 + C.x^46 + C.x^4 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^7 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7l ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^7 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 
+

 2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
x

^47 + C.x^46 + C.x^4 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^7 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 
+

....:  2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
x

....: ^47 + C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_

 decomposition_g0_g8         decomposition_g8_p2th_power decomposition_omega0_omega8

 decomposition_g0_p2th_power decomposition_g8_pth_power  decomposition_omega8_hpdh  

 decomposition_g0_pth_power  decomposition_omega0_hpdh                              



 [?7h[?12l[?25h[?25l[?7lg0_g8

 decomposition_g0_g8        





 <unknown> [?7h[?12l[?25h[?25l[?7l8p2th_power

 decomposition_g0_g8         decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7lth_power

 decomposition_g8_p2th_power

 decomposition_g8_pth_power [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g8_pth_power(ff)

[?7h[?12l[?25h[?2004ldecomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
---------------------------------------------------------------------------
ArithmeticError                           Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 decomposition_g8_pth_power(ff)

File <string>:62, in decomposition_g8_pth_power(fct, prec)

File <string>:14, in __init__(self, C, g)

File <string>:228, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    986 try:
    987     if '/' in element:
--> 988         element = sage_eval(element,d)
    989     else:
    990         element = element.replace("^","**")

File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
    196     return locals['_sage_eval_returnval_']
    197 else:
--> 198     return eval(source, sage.all.__dict__, locals)

File <string>:1, in <module>

File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
    164 elif hasattr(x, 'O'):
    165     return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))

ArithmeticError: O(y^53) not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g8_pth_power(ff)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g8_pth_power(ff, prec = 200)

[?7h[?12l[?25h[?2004ldecomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
---------------------------------------------------------------------------
ArithmeticError                           Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 decomposition_g8_pth_power(ff, prec = Integer(200))

File <string>:62, in decomposition_g8_pth_power(fct, prec)

File <string>:14, in __init__(self, C, g)

File <string>:228, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    986 try:
    987     if '/' in element:
--> 988         element = sage_eval(element,d)
    989     else:
    990         element = element.replace("^","**")

File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
    196     return locals['_sage_eval_returnval_']
    197 else:
--> 198     return eval(source, sage.all.__dict__, locals)

File <string>:1, in <module>

File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
    164 elif hasattr(x, 'O'):
    165     return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))

ArithmeticError: O(y^203) not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 
+

....:  2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
x

....: ^47 + C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.pth_root()

 

 [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^3 + 2*t^9 + t^11 + t^13 + t^15 + t^17 + 2*t^21 + O(t^23)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7laf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7luf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lrf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lef.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lnf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ltf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l_f.expansion_at_infty()[?7h[?12l[?25h[?25l[?7laf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lnf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7laf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7llf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lyf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ltf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lif.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l_f.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lpf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7laf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lrf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ltf.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l(f.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(ff.expansion_at_infty())

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(ff.expansion_at_infty())[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(ff.expansion_at_infty())

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(ff.expansion_at_infty())[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/tests/auxilliary_decompositions_test.sage')[?7h[?12l[?25h[?25l[?7l(uperelliptic_drw/tests/auxilliary_decompositions_test.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/superelliptic_

 sup…perelliptic_drw_auxilliaries.sage sup…perelliptic_drw_form.sage        

 sup…perelliptic_drw_cech.sage         sup…perelliptic_witt.sage            





 [?7h[?12l[?25h[?25l[?7ldrw_auxilliaries.sage

 sup…perelliptic_drw_auxilliaries.sage



 <unknown> [?7h[?12l[?25h[?25l[?7l'





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/superelliptic_drw_auxilliaries.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7laurent_analytic_part(ff.expansion_at_infty())[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty)[?7h[?12l[?25h[?25l[?7ldecomosition_g8_pth_power(ff, prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l, prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g8_pth_power(ff)

[?7h[?12l[?25h[?2004ldecomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
[?7h(((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y,
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7ldecomposition_g8_pth_power(ff)[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7laurent_analytic_part(ff.expansion_at_infty())[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty)[?7h[?12l[?25h[?25l[?7ldecomosition_g8_pth_power(ff, prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x^73 + C.x^72 + 2*C.x^71 + 2*C.x^70 
+

....:  2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 + C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
x

....: ^47 + C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7l1)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

 

 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lBC.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
decomposition_omega8_hpdh ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)

File <string>:103, in coordinates(self, basis)

File <string>:83, in div_by_p(self)

File <string>:33, in decomposition_omega8_hpdh(omega, prec)

NameError: name 'T' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/superelliptic_drw_auxilliaries.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(it.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)

[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
decomposition_omega8_hpdh ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
omega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
decomposition_g8_p2th_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
decomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
decomposition_g8_pth_power 0
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
[?7h[4, 1, 3, 2, 1, 8, 1, 2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().diffn().epansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().diffn().expansion_at_infty(prec = 220)

  C.a_number                               C.cartier_matrix                         C.de_rham_basis                           

  C.base_ring                              C.characteristic                         C.degrees_de_rham0                        

  C.basis_de_rham_degrees                  C.cohomology_of_structure_sheaf_basis    C.degrees_de_rham1                       >

  C.basis_holomorphic_differentials_degree C.crystalline_cohomology_basis           C.degrees_holomorphic_differentials       

 [?7h[?12l[?25h[?25l[?7la_number

 C.a_number                              







 <unknown> [?7h[?12l[?25h[?25l[?7lcartier_matrix

 C.a_number                               C.cartier_matrix                        [?7h[?12l[?25h[?25l[?7lde_rhambsis

 C.cartier_matrix                         C.de_rham_basis                         [?7h[?12l[?25h[?25l[?7lrfrobenius_matrix

 cartier_matrixde_rhambsis rfrobenius_matrix

 characteristicdegees_de_rham0x              

<cohomology_ofstructure_sheaf_basisdegrees_derham1                   y_w            

 crystalline_coomology_basis          degrees_holomrphic_differentialsexponnt                         [?7h[?12l[?25h[?25l[?7lfct_field

de_rhambsis rfrobenius_matrixfct_field          

degees_de_rham0x              final_type

degrees_derham1                   y_w            frobenius_matrix

degrees_holomrphic_differentialsexponnt                         genus   [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis

rfrobenius_matrixfct_field          holomorphic_differentials_basis

x              final_typeis_smooth 

y_w            frobenius_matrixnb_of_ptat_infty

exponnt                         genus   one  [?7h[?12l[?25h[?25l[?7lp_rank

fct_field          holomorphic_differentials_basisp_rank                         

final_typeis_smooth polynmial

frobenius_matrixnb_of_ptat_inftyuniformizer       

genus   one  verschiebung_matrix[?7h[?12l[?25h[?25l[?7lx

holomorphic_differentials_basisp_rank                         x      

is_smooth polynmialy          

nb_of_ptat_inftyuniformizer                                                 

one  verschiebung_matrix                                          [?7h[?12l[?25h[?25l[?7lp_rank

 C.p_rank                                 C.x                                     [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis

 C.holomorphic_differentials_basis        C.p_rank                                [?7h[?12l[?25h[?25l[?7lfct_field

fct_field                      holomorphic_differentials_basisp_rank 

final_typeis_smoth polynomial 

frobeniumatrix  nb_of_pts_at_infty C.uniformizer                           >

genusone                 C.verschiebung_matrix                    [?7h[?12l[?25h[?25l[?7ldr_frobenius_matrix

dr_frobenius_matrixfct_field                      holomorphic_differentials_basis

dx        final_typeis_smoth 

dy_w            frobeniumatrix  nb_of_pts_at_infty

exponentgenusone                [?7h[?12l[?25h[?25l[?7lerham_basis

erham_basis      dr_frobenius_matrixfct_field                      

egrees_de_rham0dx        final_type

egrees_de_rham1dy_w            frobeniumatrix  

degres_holomorphic_differentialsexponentgenus[?7h[?12l[?25h[?25l[?7lcartiermtrix

cartiermtrixerham_basis      dr_frobenius_matrix

chaacteristic  egrees_de_rham0dx        

cohomologyof_structure_sheaf_basisegrees_de_rham1dy_w            

crystalline_chomology_basis     degres_holomorphic_differentialsexponent[?7h[?12l[?25h[?25l[?7la_number

 a_number      cartiermtrixerham_basis      

 base_ring     chaacteristic  egrees_de_rham0

 basis_de_rhamdegrees              cohomologyof_structure_sheaf_basisegrees_de_rham1

 basis_holomorpic_differentials_degreecrystalline_chomology_basis     degres_holomorphic_differentials[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbase_ring

 C.a_number                              

 C.base_ring                             [?7h[?12l[?25h[?25l[?7lis_de_rham_degrees



 C.base_ring                             

 C.basis_de_rham_degrees                 [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_degree





 C.basis_de_rham_degrees                 

 C.basis_holomorphic_differentials_degree[?7h[?12l[?25h[?25l[?7lcrtier_matrix

 C.cartier_matrix                        





 C.basis_holomorphic_differentials_degree[?7h[?12l[?25h[?25l[?7lharacteristc

 C.cartier_matrix                        

 C.characteristic                        [?7h[?12l[?25h[?25l[?7lartier_matrx

 C.cartier_matrix                        

 C.characteristic                        [?7h[?12l[?25h[?25l[?7la_number

 C.a_number                               C.cartier_matrix                        [?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().diffn().epansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lor i i lau.expoents():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status
On branch master
Your branch is up to date with 'origin/master'.

Changes to be committed:
  (use "git restore --staged <file>..." to unstage)
	modified:   sage/.run.term-0.term
	modified:   sage/superelliptic/superelliptic_class.sage
	modified:   sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
	modified:   sage/superelliptic_drw/superelliptic_drw_cech.sage
	modified:   sage/tests.sage

Untracked files:
  (use "git add <file>..." to include in what will be committed)
	.crystalline_p2.ipynb.sage-jupyter2
	.deRhamComputation.ipynb.sage-jupyter2
	.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
	.git.x11-0.term
	.superelliptic.ipynb.sage-jupyter2
	.superelliptic_alpha.ipynb.sage-jupyter2
	.superelliptic_arbitrary_field.ipynb.sage-jupyter2
	git.x11
	sage/auxilliaries/laurent_analytic_part.sage
	sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
	sage/drafty/2gpcovers.sage
	sage/drafty/as_cartier.sage
	sage/drafty/better_trace.sage
	sage/drafty/cartier_image_representation.sage
	sage/drafty/convert_superelliptic_into_AS.sage
	sage/drafty/draft4.sage
	sage/drafty/draft5.sage
	sage/drafty/draft6.sage
	sage/drafty/draft7.sage
	sage/drafty/draft8.sage
	sage/drafty/draft_klein_covers.sage
	sage/drafty/lift_to_de_rham.sage
	sage/drafty/pole_numbers.sage
	sage/superelliptic/frobenius_kernel.sage
	sage/superelliptic/tests/expansion_at_infty.sage
	sage/superelliptic_drw/regular_form.sage
	sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage
	superelliptic_arbitrary_field.ipynb

]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sage add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sagesage/auxilliaries/laurent_analytic_part.sage sage/auxilliaries/laurent_analytic_part.sage
^C
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sage add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sagegit status

sage add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage
 add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$  add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/sup
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$  add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/supe
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$  add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/super
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ g add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/supe[1@r
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ i add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/sup[1@e
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ t add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su[1@p
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ 


]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""d"z"i"a"l"a" ""j"a" "w"s"p"o"l"r"z"e"d"n"e" "c"r"y"s"t"a"l"l"i"n"e" "c"o"h"o"m"o"l"o"g"y"!"!"!"!"
git commit -m "dzialaja wspolrzedne crystalline cohomologygit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sagegit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage"
[master a9d055a] dzialaja wspolrzedne crystalline cohomologygit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sagegit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage
 9 files changed, 1398 insertions(+), 27 deletions(-)
 create mode 100644 sage/auxilliaries/laurent_analytic_part.sage
 create mode 100644 sage/superelliptic/tests/expansion_at_infty.sage
 create mode 100644 sage/superelliptic_drw/regular_form.sage
 create mode 100644 sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 29, done.
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Counting objects: 100% (29/29), done.
Delta compression using up to 4 threads
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Compressing objects: 100% (17/17), done.
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Writing objects: 100% (17/17), 11.83 KiB | 84.00 KiB/s, done.
Total 17 (delta 11), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   995d5f0..a9d055a  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sacd sage/
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l[?7h[4 6]
[1 4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

[?7h[?12l[?25h[?2004l[?7h[1 0]
[0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l = sperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:19, in <module>

File <string>:10, in crystalline_matrix(C)

File <string>:39, in crystalline_cohomology_basis(self, prec)

File <string>:29, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:19, in <module>

File <string>:10, in crystalline_matrix(C)

File <string>:39, in crystalline_cohomology_basis(self, prec)

File <string>:29, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:19, in <module>

File <string>:16, in crystalline_matrix(C, prec)

TypeError: superelliptic_drw_cech.coordinates() got an unexpected keyword argument 'prec'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 0 0 0 0 6 0]
[1 1 0 3 0 6 6 0]
[1 2 1 6 6 3 6 6]
[4 3 3 1 0 0 3 0]
[4 1 3 2 1 8 1 2]
[8 3 3 4 0 1 7 3]
[3 6 3 3 0 0 1 6]
[4 1 6 7 0 3 3 1]
[1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0]
[0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ loasage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File <string>:235, in reduction(C, g)

File /ext/sage/9.7/src/sage/arith/misc.py:1971, in xgcd(a, b)
   1970 try:
-> 1971     return a.xgcd(b)
   1972 except AttributeError:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:19, in <module>

File <string>:10, in crystalline_matrix(C, prec)

File <string>:39, in crystalline_cohomology_basis(self, prec)

File <string>:26, in de_rham_witt_lift(cech_class, prec)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100))

File <string>:39, in crystalline_cohomology_basis(self, prec)

File <string>:24, in de_rham_witt_lift(cech_class, prec)

File <string>:6, in de_rham_witt_lift_form0(omega)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:82, in __pow__(self, exp)

File <string>:14, in __init__(self, C, g)

File <string>:228, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_()
    338     return repr(self.numer())
    339 else:
--> 340     numer_s = repr(self.numer())
    341     denom_s = repr(self.denom())
    342     if '-' in numer_s or '+' in numer_s:

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
 ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1].omega8 + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].reguler_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 B[Integer(0)].reguler_form()

AttributeError: 'superelliptic_drw_cech' object has no attribute 'reguler_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].reguler_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr_form()[?7h[?12l[?25h[?25l[?7lar_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[0].regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 B[Integer(0)].regular_form()

AttributeError: 'superelliptic_drw_cech' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B0 = B[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B0.

 B0.coordinates B0.f           B0.omega8     

 B0.curve       B0.is_regular  B0.r          

 B0.div_by_p    B0.omega0      B0.reduce     



 [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B0.omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystallinechomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lin)[?7h[?12l[?25h[?25l[?7linf)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100, info = 1)

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
 ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[0].regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l].regular_form()[?7h[?12l[?25h[?25l[?7l[].regular_form()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 B[Integer(0)].omega0.regular_form()

File <string>:81, in regular_drw_form(omega)

AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohmology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100, info = 1)

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l[0].omega0.regular_frm()[?7h[?12l[?25h[?25l[?7l0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V((x^21 + 2*x^19 + 2*x^15 + x^13) dy) + dV((2*x^15 + x^13 + 2*x^9 + x^7)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l1].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[1].omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x] d[y] + V((0) dy) + dV((x^6 + 2*x^4)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohmology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100, info = 1)

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l[1].omega0.regular_frm()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 B[Integer(0)].regular_form()

File <string>:90, in regular_drw_cech(cocycle)

TypeError: can only concatenate str (not "superelliptic_regular_drw_form") to str
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l7].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[7].omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x^4] d[y] + V((0) dy) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_cech(cocycle):

....:     print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")

....: 

....: superelliptic_drw_cech.regular_form = regular_drw_cech[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_cech(cocycle):

....:     print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")

....: 

....: superelliptic_drw_cech.regular_form = regular_drw_cech

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[7].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lgular_form()[?7h[?12l[?25h[?25l[?7lsage: B[0].regular_form()

[?7h[?12l[?25h[?2004l( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lor i i lau.expoents():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i in range(8):

....: [?7h[?12l[?25h[?25l[?7lprint("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(B[i].regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(8):

....:     print(B[i].regular_form())

....: 

[?7h[?12l[?25h[?2004l( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
None
( [0] d[x] + [x] d[y] + V((2*x^36 + x^28 + x^12 + 2*x^4) dy) + dV((x^12 + 2*x^4)*y), V(((x^8 + 1)/x^4)*y) )
None
( [0] d[x] + [x^2] d[y] + V((x^63 + 2*x^55 + 2*x^39 + x^31) dy) + dV((2*x^39 + x^31 + 2*x^15 + x^7)*y), V(((x^8 + 1)/x)*y) )
None
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [18], in <cell line: 1>()
      1 for i in range(Integer(8)):
----> 2     print(B[i].regular_form())

Input In [16], in regular_drw_cech(cocycle)
      1 def regular_drw_cech(cocycle):
----> 2     print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")

File <string>:80, in regular_drw_form(omega)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:84, in __add__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:28, in __sub__(self, other)

File <string>:7, in __init__(self, C, g)

File <string>:252, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:647, in PolynomialRing(base_ring, *args, **kwds)
    644         raise TypeError("variable names specified twice inconsistently: %r and %r" % (names, kwnames))
    646 if multivariate or len(names) != 1:
--> 647     return _multi_variate(base_ring, names, **kwds)
    648 else:
    649     return _single_variate(base_ring, names, **kwds)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:762, in _multi_variate(base_ring, names, sparse, order, implementation)
    760 from sage.rings.polynomial.term_order import TermOrder
    761 n = len(names)
--> 762 order = TermOrder(order, n)
    764 # "implementation" must be last
    765 key = [base_ring, names, n, order, implementation]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in range(8):

....:     print(B[i].regular_form())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lprintB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7l....: 

....:     B[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()

 [?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7l B[i].regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(8):

....:     B[i].regular_form()

....: 

[?7h[?12l[?25h[?2004l( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
( [0] d[x] + [x] d[y] + V((2*x^36 + x^28 + x^12 + 2*x^4) dy) + dV((x^12 + 2*x^4)*y), V(((x^8 + 1)/x^4)*y) )
( [0] d[x] + [x^2] d[y] + V((x^63 + 2*x^55 + 2*x^39 + x^31) dy) + dV((2*x^39 + x^31 + 2*x^15 + x^7)*y), V(((x^8 + 1)/x)*y) )
( [0] d[x] + [x^3] d[y] + V((0) dy) + dV(0), V((x^10 + x^2)*y) )
( [0] d[x] + [x^7] d[y] + V((x^54 + 2*x^46 + 2*x^30 + x^22) dy) + dV((2*x^30 + x^22)*y), [2/x*y] + V(((x^24 + x^16 + x^8 + 2)/x^2)*y) )
( [0] d[x] + [2*x^6] d[y] + V((0) dy) + dV((2*x^27 + x^19)*y), [2/x^2*y] + V((2*x^19 + 2*x^11 + 2*x^3)*y) )
( [0] d[x] + [0] d[y] + V((x^72 + 2*x^64 + 2*x^48 + x^40) dy) + dV((2*x^48 + x^40 + 2*x^24 + x^16)*y), [2/x^3*y] )
( [0] d[x] + [x^4] d[y] + V((0) dy) + dV(0), [2/x^4*y] + V(((x^16 + x^8 + 1)/x^3)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(x^3 + x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l`[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 B1 = C1.crystalline_cohomology_basis(prec = Integer(100), info = Integer(1))

File <string>:41, in crystalline_cohomology_basis(self, prec, info)

File <string>:33, in de_rham_witt_lift(cech_class, prec)

File <string>:6, in __init__(self, omega0, f)

File <string>:90, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:65, in __mul__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:7, in __init__(self, C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
    704 x0, y0 = x, y
    705 try:
--> 706     x, y = resolve_fractions(x0, y0)
    707 except (AttributeError, TypeError):
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))

File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
    686 yd = y.denominator()
    687 try:
--> 688     return (xn * yd, yn * xd)
    689 except (AttributeError, TypeError, ValueError):
    690     pass

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1198 # Now coerce to a common parent and do the operation there
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:
   1202     self._record_exception()

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1309 x_map, y_map = coercions
   1310 if x_map is not None:
-> 1311     x_elt = (<Map>x_map)._call_(x)
   1312 else:
   1313     x_elt = x

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    196 var = R.variable_name()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 else:
    200     return R([self])

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    417 w = {remove_from_tuple(e, ind): val
    418      for e, val in self.dict().iteritems() if not e[ind]}
--> 419 v = [B(w)]  # coefficients that don't involve var
    420 z = var
    421 for i in range(1,d+1):

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:309, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    306     args = (self.base_ring(), self.variable_names(), None, self.is_sparse())
    307     return unpickle_PolynomialRing, args
--> 309 def _element_constructor_(self, x=None, check=True, is_gen=False,
    310                           construct=False, **kwds):
    311     r"""
    312     Convert ``x`` into this univariate polynomial ring,
    313     possibly non-canonically.
   (...)
    412         λ^2
    413     """
    414     C = self.element_class

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(8):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l i in range(8):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l):[?7h[?12l[?25h[?25l[?7l2):[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for i in range(2):

....: [?7h[?12l[?25h[?25l[?7lprint(B[i].regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l(B[i].regular_form())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l1[i].regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(B1[i].regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(2):

....:     print(B1[i].regular_form())

....: 

[?7h[?12l[?25h[?2004l( [0] d[x] + [2] d[y] + V((x^21 + x^19 + x^15 + x^13) dy) + dV((x^15 + x^13 + 2*x^9 + 2*x^7)*y), V(((x^2 + 2)/x)*y) )
None
( [0] d[x] + [2*x] d[y] + V((0) dy) + dV((2*x^6 + 2*x^4)*y), [2/x*y] + V((x^4 + 2*x^2 + 1)*y) )
None
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-1)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lxpansion[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(x^63 + 2*x^55 + 2*x^39 + x^31)[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, x, 1, x, 2, 0, 1, x, 1, x, 0, 0, 2, 0, 0, 0, 1, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^3 - x, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt.<t> = LaurentSeriesRing(F, default_prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rxt.<t> = PolynomialRing(Rx)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt.<t> = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7ladic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcadic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l=adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: coo = adic_expansion(x^3 - x, x^3 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcoo = adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7lRxt.<t> = PolynomalRing(Rx)[?7h[?12l[?25h[?25l[?7ladic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l(x^63+ 2*x^55+ 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcadic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l=adic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: coo = adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(2):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li in range(2):[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lenumerate[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i, a in enumerate(coo):

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lenumerat[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: FF = Rxt(0)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(2):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = Rxt(0)[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsum[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lenumerate[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: FF = sum(a*t^i for i, a in enumerate(coo))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = sum(a*t^i for i, a in enumerate(coo))[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lsage: FF

[?7h[?12l[?25h[?2004l[?7ht^21 + t^19 + 2*t^15 + x*t^12 + t^11 + x*t^10 + t^9 + 2*t^7 + x*t^6 + t^5 + x*t^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((x/y) dx, 0, (x/y) dx),
 ((x^2/y) dx, 0, (x^2/y) dx),
 ((x^3/y) dx, 0, (x^3/y) dx),
 ((x^7/y) dx, 2/x*y, ((-1)/(x*y)) dx),
 (((-x^6)/y) dx, 2/x^2*y, 0 dx),
 (0 dx, 2/x^3*y, (1/(x^3*y)) dx),
 ((x^4/y) dx, 2/x^4*y, ((-1)/(x^4*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ly^2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^3).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-3 + t^13 + O(t^17)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-7 + O(t^13)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^4).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-1 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l5).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^5).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + 2*t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^5).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^5).diffn()

[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l7).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^7).diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^8 - 1)/(x^7*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^7).diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx - a(-2)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^5*C.y.diffn()).int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 (C.x**Integer(5)*C.y.diffn()).int()

File <string>:198, in int(self)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
   3992 cdef Py_ssize_t n
   3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
   3996 return S(p)

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^5*C.y.diffn()).int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^5*C.y.diffn()).cartier()

[?7h[?12l[?25h[?2004l[?7h(x^4/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^5*C.y.diffn()).cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^5*C.y.diffn()).cartier().inv_cartier()

[?7h[?12l[?25h[?2004l[?7h((x^21 - x^13)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^5*C.y.diffn()).cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l *C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l-*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l *C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lC*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l.*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lx*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l^*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l3*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l()*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x^5 - C.x^3)*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x^5 - C.x^3)*C.y.diffn()).cartier()

[?7h[?12l[?25h[?2004l[?7h(x^4/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l7, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^7, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[x, 2*x^2 + 1, x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt.<t> = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^7, x^3 - x)[?7h[?12l[?25h[?25l[?7l((C.x^5 - C.x^3)*C.y.diffn()).cartier()[?7h[?12l[?25h[?25l[?7lC.x^5*C.y.diffn()).cartier(inv_catier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7ly/C.x^7).difn()[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lexpasion_at_infty()[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lFF[?7h[?12l[?25h[?25l[?7l = sum(a*t^i for i, a in enumerate(coo))[?7h[?12l[?25h[?25l[?7lRxt0)[?7h[?12l[?25h[?25l[?7lcoo = adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7lFF = Rxt(0)[?7h[?12l[?25h[?25l[?7lsuma*t^i for i, a in enumerate(coo))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lenumerat[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx[?7h[?12l[?25h[?25l[?7lsage: x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(parent(lau))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt.<t> = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12, in <module>

File <string>:41, in crystalline_cohomology_basis(self, prec, info)

File <string>:29, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [48], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12, in <module>

File <string>:41, in crystalline_cohomology_basis(self, prec, info)

File <string>:32, in de_rham_witt_lift(cech_class, prec)

File <string>:36, in decomposition_omega0_omega8(omega, prec)

File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
    583     return expression.sum(*args, **kwds)
    584 elif max(len(args),len(kwds)) <= 1:
--> 585     return sum(expression, *args, **kwds)
    586 else:
    587     from sage.symbolic.ring import SR

File <string>:36, in <genexpr>(.0)

File <string>:156, in residue(self, place, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:11, in <module>

File <string>:41, in crystalline_cohomology_basis(self, prec, info)

File <string>:25, in de_rham_witt_lift(cech_class, prec)

File <string>:15, in de_rham_witt_lift_form8(omega)

File <string>:90, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:65, in __mul__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:7, in __init__(self, C, g)

File <string>:271, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1007 try:
   1008     # now try calling the base ring's __call__ methods
-> 1009     element = self.base_ring()(element)
   1010     _p = p_NSet(sa2si(element,_ring), _ring)
   1011     return new_MP(self,_p)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    378 else:
    379     try:
--> 380         z = integer_ring.Z(value)
    381     except (TypeError, ValueError):
    382         from sage.structure.element import Expression

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    829     return R(self.__numerator)
    830 else:
--> 831     self.reduce()
    832     num = R(self.__numerator)
    833     inv_den = R(self.__denominator).inverse_of_unit()

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
   1237 if self._is_reduced:
   1238     return
-> 1239 super(self.__class__, self).reduce()
   1240 self.normalize_leading_coefficients()
   1241 

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    162     return codomain.coerce(nnum/nden)
    163 
--> 164 cpdef reduce(self):
    165     """
    166     Reduce this fraction.

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    195     return
    196 try:
--> 197     g = self.__numerator.gcd(self.__denominator)
    198     if not g.is_unit():
    199         self.__numerator //= g

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4911         raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
   4912     else:
-> 4913         return doit(self, other)
   4914 
   4915 @coerce_binop

File /ext/sage/9.7/src/sage/rings/fraction_field.py:944, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
    942 Pol = f.parent()
    943 Num = Pol.change_ring(self.base())
--> 944 f1 = Num(f.numerator())
    945 g1 = Num(g.numerator())
    946 return Pol(f1.gcd(g1)).monic()

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:452, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    450     except NameError:
    451         raise TypeError("Unable to coerce string")
--> 452 elif isinstance(x, FractionFieldElement):
    453     if x.denominator().is_unit():
    454         x = x.numerator() * x.denominator().inverse_of_unit()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7ltryL[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: try:

....: [?7h[?12l[?25h[?25l[?7lprint(B1[i].regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:     print(0/0)

....: [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()

 [?7h[?12l[?25h[?25l[?7l()e[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lexcept[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lIndexError[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....: except IndexError:

....: [?7h[?12l[?25h[?25l[?7lprint(B1[i].regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l"( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:     print("a")

....: [?7h[?12l[?25h[?25l[?7lsage: try:

....:     print(0/0)

....: except IndexError:

....:     print("a")

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [50], in <cell line: 1>()
      1 try:
----> 2     print(Integer(0)/Integer(0))
      3 except IndexError:
      4     print("a")

File /ext/sage/9.7/src/sage/rings/integer.pyx:2022, in sage.rings.integer.Integer.__truediv__()
   2020 if type(left) is type(right):
   2021     if mpz_sgn((<Integer>right).value) == 0:
-> 2022         raise ZeroDivisionError("rational division by zero")
   2023     x = <Rational> Rational.__new__(Rational)
   2024     mpq_div_zz(x.value, (<Integer>left).value, (<Integer>right).value)

ZeroDivisionError: rational division by zero
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: try:

....:     print(0/0)

....: except IndexError:

....:     print("a")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lIndeError:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lZEror:[?7h[?12l[?25h[?25l[?7leEror:[?7h[?12l[?25h[?25l[?7lrEror:[?7h[?12l[?25h[?25l[?7loEror:[?7h[?12l[?25h[?25l[?7lDEror:[?7h[?12l[?25h[?25l[?7liEror:[?7h[?12l[?25h[?25l[?7lvEror:[?7h[?12l[?25h[?25l[?7liEror:[?7h[?12l[?25h[?25l[?7lsEror:[?7h[?12l[?25h[?25l[?7liEror:[?7h[?12l[?25h[?25l[?7loEror:[?7h[?12l[?25h[?25l[?7lZeroDivisionError:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print("a")

....: [?7h[?12l[?25h[?25l[?7lsage: try:

....:     print(0/0)

....: except ZeroDivisionError:

....:     print("a")

....: 

[?7h[?12l[?25h[?2004la
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:60, in __mul__(self, other)

File <string>:14, in __init__(self, C, g)

File <string>:228, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1002 try:
-> 1003     return self(str(element))
   1004 except TypeError:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    990         element = element.replace("^","**")
--> 991         element = eval(element, d, {})
    992 except (SyntaxError, NameError):

File <string>:1, in <module>

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12, in <module>

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:26, in de_rham_witt_lift(cech_class, prec)

File <string>:90, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:149, in auxilliary_derivative(P)

File <string>:147, in auxilliary_derivative(P)

File <string>:35, in __sub__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ gcd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status
On branch master
Your branch is up to date with 'origin/master'.

Changes not staged for commit:
  (use "git add <file>..." to update what will be committed)
  (use "git restore <file>..." to discard changes in working directory)
	modified:   sage/.run.term-0.term
	modified:   sage/drafty/draft.sage
	modified:   sage/superelliptic_drw/de_rham_witt_lift.sage
	modified:   sage/superelliptic_drw/regular_form.sage
	modified:   sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
	modified:   sage/superelliptic_drw/superelliptic_drw_cech.sage

Untracked files:
  (use "git add <file>..." to include in what will be committed)
	.crystalline_p2.ipynb.sage-jupyter2
	.deRhamComputation.ipynb.sage-jupyter2
	.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
	.git.x11-0.term
	.superelliptic.ipynb.sage-jupyter2
	.superelliptic_alpha.ipynb.sage-jupyter2
	.superelliptic_arbitrary_field.ipynb.sage-jupyter2
	git.x11
	sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
	sage/drafty/2gpcovers.sage
	sage/drafty/as_cartier.sage
	sage/drafty/better_trace.sage
	sage/drafty/cartier_image_representation.sage
	sage/drafty/convert_superelliptic_into_AS.sage
	sage/drafty/draft4.sage
	sage/drafty/draft5.sage
	sage/drafty/draft6.sage
	sage/drafty/draft7.sage
	sage/drafty/draft8.sage
	sage/drafty/draft_klein_covers.sage
	sage/drafty/lift_to_de_rham.sage
	sage/drafty/pole_numbers.sage
	sage/superelliptic/frobenius_kernel.sage
	superelliptic_arbitrary_field.ipynb

no changes added to commit (use "git add" and/or "git commit -a")
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit - mm ""p"r"z"e"d" "z"m"i"n"a"""a"n"a" "w" "e"x"p"a"n"s"i"o"n" "a"t" "i"n"f"t"y" "w" "s"u"p"e"r"e"l"l"i"p"t"i"c"
[master eda1cca] przed zmiana w expansion at infty w superelliptic
 6 files changed, 1599 insertions(+), 62 deletions(-)
 rewrite sage/drafty/draft.sage (94%)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 21, done.
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Counting objects: 100% (21/21), done.
Delta compression using up to 4 threads
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Writing objects: 100% (11/11), 12.06 KiB | 81.00 KiB/s, done.
Total 11 (delta 9), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   a9d055a..eda1cca  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage/; sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: load('tests

 tests     

 tests.sage





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 tests     



 <unknown> [?7h[?12l[?25h[?25l[?7l.





[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lExpansion at infty test:
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('tests.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:3, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:7, in <module>

NameError: name 'superelliptic' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lExpansion at infty test:
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('tests.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:3, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:8, in <module>

File <string>:120, in expansion_at_infty(self, place, prec)

NameError: name 'fct' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lExpansion at infty test:
---------------------------------------------------------------------------
UnboundLocalError                         Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('tests.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:3, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:8, in <module>

File <string>:115, in expansion_at_infty(self, place, prec)

UnboundLocalError: local variable 'f' referenced before assignment
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lExpansion at infty test:
True
True True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:11, in <module>

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:29, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File <string>:143, in expansion_at_infty(self, place, prec)

TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:11, in <module>

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:29, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File <string>:143, in expansion_at_infty(self, place, prec)

TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly^2[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 C.y.diffn().expansion_at_infty()

File <string>:143, in expansion_at_infty(self, place, prec)

TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Input In [11] in <cell line: 1>
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:3 in <module>

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:144
    dx_series = C.x_series[place = place]
                           ^
SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:11, in <module>

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:29, in de_rham_witt_lift(cech_class, prec)

File <string>:7, in decomposition_g0_g8(fct, prec)

File <string>:107, in coordinates(self, basis, basis_holo, prec)

File <string>:79, in serre_duality_pairing(self, fct, prec)

File <string>:145, in expansion_at_infty(self, place, prec)

TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 C.y.diffn().expansion_at_infty()

File <string>:145, in expansion_at_infty(self, place, prec)

TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:11, in <module>

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:32, in de_rham_witt_lift(cech_class, prec)

File <string>:37, in decomposition_omega0_omega8(omega, prec)

ValueError: (((4*x^50 + x^46 + 2*x^44 + 2*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + x^32 + 2*x^28 + 3*x^22 + 4*x^18 + x^16 + x^14 + x^12 + 3*x^10 + 3*x^6 + 4*x^4 + 1)/(x^30 + 3*x^28 + 3*x^26 + x^24))*y) dx has non zero residue!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y*C.y.diffn()

[?7h[?12l[?25h[?2004l[?7h(-2*x^2 + 1) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y*C.y.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y*C.y.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    493 """
--> 494 return self.getattr_from_category(name)
    495 

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    506     cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
    508 

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'form'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 Integer(2)*C.y*C.y.diffn().expansion_at_infty()

File <string>:63, in __mul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y*C.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.y*C.y.difn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (2*C.y*C.y.diffn()).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h3*t^-6 + 2*t^-2 + 4*t^2 + t^6 + 4*t^10 + 3*t^14 + 2*t^18 + 3*t^22 + 2*t^26 + 3*t^30 + 4*t^34 + t^38 + 4*t^42 + t^46 + 4*t^50 + O(t^94)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.y*C.y.diffn()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l ).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l ).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (-C.x).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-C.dx).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lxexpasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x.difn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -C.x.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?7ht^-3 + 4*t + 4*t^5 + 3*t^9 + t^17 + 3*t^21 + 3*t^25 + t^29 + 3*t^37 + 4*t^41 + 4*t^45 + 3*t^49 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lxdiff().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lyprec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyC.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7lyC.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l C.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l=C.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l C.y.expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2- (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l- (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 - xx)

[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 3*t^2 + 3*t^6 + t^10 + 2*t^18 + t^22 + t^26 + 2*t^30 + t^38 + 3*t^42 + 3*t^46 + t^50 + O(t^94)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 - xx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x)[?7h[?12l[?25h[?25l[?7l+ x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 + xx)

[?7h[?12l[?25h[?2004l[?7hO(t^94)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lyprec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiff().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h4*t^-3 + t^5 + 2*t^9 + 4*t^17 + 2*t^21 + 2*t^25 + 4*t^29 + 2*t^37 + t^41 + t^45 + 2*t^49 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 + xx)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^2 - 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lxexpasion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiff().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.diffn()

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.diffn().expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: B1

[?7h[?12l[?25h[?2004l[?7h[([(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y), [(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^34 + 4*x^32 + 4*x^30 + 3*x^28 + 3*x^26 + 3*x^24 + 2*x^22 + 4*x^20 + 4*x^16 + x^14 + x^12 + 3*x^10 + x^8 + 4*x^6 + 3*x^4 + x^2 + 2)/(x^42 + 2*x^38 + 3*x^34 + 3*x^32 + 4*x^30 + 2*x^28 + 2*x^22 + x^18 + 3*x^12 + 4*x^10 + x^8 + 3*x^6 + x^4))*y])),
 ([(1/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 - 2*x^31 + 2*x^25 - 2*x^23 + x^21 - 2*x^19 + x^17 - x^15 - x^13 + 2*x^11 - 2*x^9 - 2*x^7 + x^5 + x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^119 + 3*x^115 + x^113 + 2*x^111 + 3*x^109 + x^105 + x^95 + 3*x^93 + 2*x^89 + 3*x^87 + 2*x^85 + 2*x^83 + 3*x^81 + 2*x^75 + x^71 + 3*x^69 + 4*x^67 + x^65 + x^63 + 3*x^61 + 2*x^53 + 3*x^49 + 3*x^47 + 2*x^41 + x^39 + 2*x^37 + 4*x^35 + 2*x^33 + 4*x^31 + 2*x^29 + 3*x^25 + 2*x^23 + 4*x^21 + 3*x^19 + 4*x^15 + 4*x^13 + 4*x^11 + 4*x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y), [(1/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 - 2*x^31 + 2*x^25 - 2*x^23 + x^21 - 2*x^19 + x^17 - x^15 - x^13 + 2*x^11 - 2*x^9 - 2*x^7 + x^5 + x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + 3*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + x^14 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 2*x^2 + 2)/(x^45 + 2*x^41 + 3*x^37 + 3*x^35 + 4*x^33 + 2*x^31 + 2*x^25 + x^21 + 3*x^15 + 4*x^13 + x^11 + 3*x^9 + x^7))*y])),
 ([(x/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 - x^34 + x^32 - 2*x^30 + 2*x^28 - x^26 - 2*x^24 - 2*x^20 - 2*x^18 - 2*x^16 + x^14 + x^12 + x^10 - 2*x^8 + x^6 + 2*x^4 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^124 + 3*x^120 + x^118 + 2*x^116 + 3*x^114 + x^110 + x^100 + 3*x^98 + 2*x^94 + 3*x^92 + 2*x^90 + 2*x^88 + 3*x^86 + 2*x^80 + x^76 + 3*x^74 + 4*x^72 + x^70 + x^68 + 3*x^66 + 2*x^58 + 3*x^54 + 3*x^52 + 2*x^46 + x^44 + 2*x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 2*x^34 + 3*x^30 + 2*x^28 + 4*x^26 + 3*x^24 + 4*x^20 + 4*x^18 + 4*x^16 + 4*x^14)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y), [(x/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 - x^34 + x^32 - 2*x^30 + 2*x^28 - x^26 - 2*x^24 - 2*x^20 - 2*x^18 - 2*x^16 + x^14 + x^12 + x^10 - 2*x^8 + x^6 + 2*x^4 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^36 + 3*x^34 + 3*x^32 + x^30 + 4*x^28 + 3*x^26 + 2*x^24 + 4*x^22 + 2*x^20 + 4*x^16 + 4*x^14 + 4*x^12 + 3*x^8 + 4*x^4 + x^2 + 2)/(x^44 + 2*x^40 + 3*x^36 + 3*x^34 + 4*x^32 + 2*x^30 + 2*x^24 + x^20 + 3*x^14 + 4*x^12 + x^10 + 3*x^8 + x^6))*y])),
 ([(x^2/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^33 + 2*x^31 + x^29 - x^27 + x^25 - x^21 - x^19 + 2*x^17 + 2*x^15 - x^13 - 2*x^11 + 2*x^9 + x^7 + 2*x^5 + x^3 + 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^129 + 3*x^125 + x^123 + 2*x^121 + 3*x^119 + x^115 + x^105 + 3*x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 2*x^85 + x^81 + 3*x^79 + 4*x^77 + x^75 + x^73 + 3*x^71 + 2*x^63 + 3*x^59 + 3*x^57 + 2*x^51 + x^49 + 2*x^47 + 4*x^45 + 2*x^43 + 4*x^41 + 2*x^39 + 3*x^35 + 2*x^33 + 4*x^31 + 3*x^29 + 4*x^25 + 4*x^23 + 4*x^21 + 4*x^19)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y), [(x^2/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^33 + 2*x^31 + x^29 - x^27 + x^25 - x^21 - x^19 + 2*x^17 + 2*x^15 - x^13 - 2*x^11 + 2*x^9 + x^7 + 2*x^5 + x^3 + 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^45 + 2*x^41 + 3*x^37 + 3*x^35 + 4*x^33 + 2*x^31 + 2*x^25 + x^21 + 3*x^15 + 4*x^13 + x^11 + 3*x^9 + x^7))*y])),
 ([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^134 + 3*x^130 + x^128 + 2*x^126 + 3*x^124 + x^120 + x^110 + 3*x^108 + 2*x^104 + 3*x^102 + 2*x^100 + 2*x^98 + 3*x^96 + 2*x^90 + x^86 + 3*x^84 + 4*x^82 + x^80 + x^78 + 3*x^76 + 2*x^68 + 3*x^64 + 3*x^62 + 2*x^56 + x^54 + 2*x^52 + 4*x^50 + 2*x^48 + 4*x^46 + 2*x^44 + 3*x^40 + 2*x^38 + 4*x^36 + 3*x^34 + 4*x^30 + 4*x^28 + 4*x^26 + 4*x^24)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])),
 ([(x^4/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 + x^31 - x^29 - 2*x^27 + 2*x^23 - x^21 + x^19 + 2*x^15 + x^13 - x^11 - x^9 + x^5 + x^3 - x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^139 + 3*x^135 + x^133 + 2*x^131 + 3*x^129 + x^125 + x^115 + 3*x^113 + 2*x^109 + 3*x^107 + 2*x^105 + 2*x^103 + 3*x^101 + 2*x^95 + x^91 + 3*x^89 + 4*x^87 + x^85 + x^83 + 3*x^81 + 2*x^73 + 3*x^69 + 3*x^67 + 2*x^61 + x^59 + 2*x^57 + 4*x^55 + 2*x^53 + 4*x^51 + 2*x^49 + 3*x^45 + 2*x^43 + 4*x^41 + 3*x^39 + 4*x^35 + 4*x^33 + 4*x^31 + 4*x^29)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y), [(x^4/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 + x^31 - x^29 - 2*x^27 + 2*x^23 - x^21 + x^19 + 2*x^15 + x^13 - x^11 - x^9 + x^5 + x^3 - x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^34 + 3*x^32 + 2*x^30 + 2*x^28 + x^26 + x^24 + 4*x^22 + 3*x^20 + x^18 + 2*x^16 + 4*x^14 + x^10 + 3*x^4 + 3*x^2 + 2)/(x^43 + 2*x^39 + 3*x^35 + 3*x^33 + 4*x^31 + 2*x^29 + 2*x^23 + x^19 + 3*x^13 + 4*x^11 + x^9 + 3*x^7 + x^5))*y])),
 ([(x^5/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^42 + x^38 - 2*x^36 - 2*x^32 + x^30 + 2*x^28 - 2*x^24 + x^22 - x^20 + 2*x^18 - 2*x^14 - 2*x^10 + 2*x^8 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^144 + 3*x^140 + x^138 + 2*x^136 + 3*x^134 + x^130 + x^120 + 3*x^118 + 2*x^114 + 3*x^112 + 2*x^110 + 2*x^108 + 3*x^106 + 2*x^100 + x^96 + 3*x^94 + 4*x^92 + x^90 + x^88 + 3*x^86 + 2*x^78 + 3*x^74 + 3*x^72 + 2*x^66 + x^64 + 2*x^62 + 4*x^60 + 2*x^58 + 4*x^56 + 2*x^54 + 3*x^50 + 2*x^48 + 4*x^46 + 3*x^44 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y), [(x^5/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^42 + x^38 - 2*x^36 - 2*x^32 + x^30 + 2*x^28 - 2*x^24 + x^22 - x^20 + 2*x^18 - 2*x^14 - 2*x^10 + 2*x^8 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^22 + x^20 + 4*x^18 + 2*x^16 + 2*x^14 + x^10 + 3*x^8 + x^6 + 2*x^2 + 2)/(x^44 + 2*x^40 + 3*x^36 + 3*x^34 + 4*x^32 + 2*x^30 + 2*x^24 + x^20 + 3*x^14 + 4*x^12 + x^10 + 3*x^8 + x^6))*y])),
 ([((3*x^12 + 3*x^8 + 3*x^2 + 4)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^77 - x^73 - 2*x^69 - x^67 - x^65 + 2*x^61 + x^59 - 2*x^57 - x^55 - x^49 + 2*x^45 + 2*x^43 + x^41 - x^37 - x^35 + 2*x^33 + x^31 + x^29 - x^25 + x^23 - x^21 + 2*x^17 - 2*x^15 - x^13 + 2*x^11 - x^7 + 2*x^5 - 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^179 + 4*x^175 + 3*x^173 + x^171 + 4*x^169 + 3*x^165 + x^159 + 2*x^155 + 2*x^153 + x^151 + 4*x^147 + 4*x^145 + x^143 + 4*x^141 + 4*x^135 + 4*x^133 + 3*x^131 + x^129 + x^127 + 3*x^125 + 2*x^123 + 4*x^121 + 2*x^119 + x^115 + x^111 + x^107 + 2*x^103 + 4*x^99 + 2*x^95 + x^91 + 3*x^89 + x^87 + 3*x^85 + 4*x^83 + 3*x^81 + x^79 + 3*x^77 + x^73 + 2*x^71 + x^67 + 3*x^65 + x^63 + 4*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + 3*x^51 + 2*x^49 + 3*x^47 + 2*x^45 + x^43 + 3*x^37 + 4*x^33 + 3*x^31 + 2*x^29 + 4*x^25 + 3*x^21 + 4*x^19 + x^15 + x^13 + x^11 + x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y), [(4/(x^16 + 2*x^12 + 3*x^8 + x^6 + 4*x^4 + 4*x^2))*y] d[x] + V(((x^40 - x^38 + 2*x^34 - 2*x^32 - 2*x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - 2*x^16 + x^14 - x^12 - 2*x^10 - 2*x^8 + 2*x^6 - 2*x^4 - x^2 + 2)/(x^41*y + 2*x^37*y - 2*x^33*y - 2*x^31*y - x^29*y + 2*x^27*y + 2*x^21*y + x^17*y - 2*x^11*y - x^9*y + x^7*y - 2*x^5*y + x^3*y)) dx) + dV([((2*x^34 + x^30 + x^28 + 2*x^26 + 3*x^24 + x^20 + 3*x^18 + x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^2 + 4)/(x^43 + 2*x^39 + 3*x^35 + 3*x^33 + 4*x^31 + 2*x^29 + 2*x^23 + x^19 + 3*x^13 + 4*x^11 + x^9 + 3*x^7 + x^5))*y])),
 ([((x^12 + 4*x^8 + 4*x^4 + x^2 + 1)/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^68 + 2*x^62 + x^60 - x^58 - 2*x^56 + x^54 - 2*x^52 + 2*x^50 - 2*x^42 - x^40 - 2*x^36 + 2*x^34 - x^32 + x^30 + 2*x^28 + x^26 + x^22 - 2*x^20 + 2*x^18 + 2*x^16 - 2*x^14 - 2*x^12 + x^10 + x^8 - x^6 + 2*x^4 + 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^174 + 3*x^170 + x^168 + 2*x^166 + 3*x^164 + x^160 + 3*x^154 + 3*x^150 + 2*x^148 + 3*x^146 + 4*x^144 + 3*x^142 + x^140 + 2*x^138 + 3*x^136 + 3*x^134 + 3*x^130 + x^128 + 4*x^126 + x^122 + x^120 + 2*x^116 + x^110 + x^106 + x^104 + x^102 + 4*x^100 + x^96 + 3*x^94 + x^86 + 3*x^84 + x^82 + x^80 + 3*x^78 + 3*x^76 + 2*x^72 + 3*x^70 + x^68 + 4*x^66 + 2*x^64 + x^62 + 3*x^60 + x^58 + 2*x^56 + 4*x^54 + x^52 + 2*x^50 + x^48 + 4*x^46 + 3*x^44 + x^40 + 2*x^36 + 2*x^32 + 3*x^30 + 4*x^26 + x^24 + 2*x^20 + x^18 + 3*x^16 + 2*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y), [(2/(x^17 + 2*x^13 + 3*x^9 + x^7 + 4*x^5 + 4*x^3))*y] d[x] + V(((x^44 - x^42 - 2*x^40 - x^36 + 2*x^34 - x^32 - x^28 + x^26 - 2*x^24 + x^20 + 2*x^18 + x^12 - 2*x^10 - x^8 + 2*x^6 - 2*x^4 - 1)/(x^46*y + 2*x^42*y - 2*x^38*y - 2*x^36*y - x^34*y + 2*x^32*y + 2*x^26*y + x^22*y - 2*x^16*y - x^14*y + x^12*y - 2*x^10*y + x^8*y)) dx) + dV([((4*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 3*x^22 + x^20 + x^14 + 2*x^10 + 3*x^6 + 2*x^2 + 2)/(x^42 + 2*x^38 + 3*x^34 + 3*x^32 + 4*x^30 + 2*x^28 + 2*x^22 + x^18 + 3*x^12 + 4*x^10 + x^8 + 3*x^6 + x^4))*y])),
 ([((4*x^10 + 3*x^2 + 4)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^67 + x^63 + 2*x^59 + 2*x^57 - 2*x^55 - 2*x^53 - 2*x^49 + x^47 - x^45 - 2*x^43 + x^41 - 2*x^39 + 2*x^37 + 2*x^35 + 2*x^33 - 2*x^27 - x^25 - x^23 - 2*x^21 + x^17 + 2*x^11 - x^9 + 2*x^5 + 2*x^3)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^169 + 2*x^165 + 4*x^163 + 3*x^161 + 2*x^159 + 4*x^155 + 4*x^145 + 2*x^143 + 3*x^139 + 2*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + x^129 + 2*x^125 + 3*x^123 + 4*x^119 + x^117 + 4*x^115 + 3*x^113 + 2*x^109 + 2*x^105 + 2*x^103 + 3*x^99 + x^97 + 3*x^93 + 2*x^91 + 2*x^89 + x^83 + x^81 + 2*x^79 + 2*x^77 + 3*x^75 + x^73 + 4*x^71 + 4*x^69 + x^67 + x^63 + 3*x^61 + 4*x^57 + 3*x^53 + x^51 + 3*x^47 + 2*x^45 + x^43 + 3*x^37 + 4*x^33 + 3*x^31 + 2*x^29 + 4*x^25 + 3*x^21 + 4*x^19 + x^15 + x^13 + x^11 + x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y), [(2/(x^16 + 2*x^12 + 3*x^8 + x^6 + 4*x^4 + 4*x^2))*y] d[x] + V(((2*x^44 + x^36 + x^34 - 2*x^32 - x^30 + x^24 + x^22 + 2*x^20 - 2*x^18 - 2*x^16 - x^14 - 2*x^12 - 2*x^10 + x^6 + x^4 - x^2 - 1)/(x^51*y + 2*x^47*y - 2*x^43*y - 2*x^41*y - x^39*y + 2*x^37*y + 2*x^31*y + x^27*y - 2*x^21*y - x^19*y + x^17*y - 2*x^15*y + x^13*y)) dx) + dV([((3*x^40 + 4*x^38 + 2*x^36 + x^34 + 2*x^32 + 2*x^30 + 3*x^26 + 2*x^24 + 3*x^22 + x^20 + x^18 + x^14 + x^12 + x^10 + 2*x^8 + 4*x^2 + 4)/(x^49 + 2*x^45 + 3*x^41 + 3*x^39 + 4*x^37 + 2*x^35 + 2*x^29 + x^25 + 3*x^19 + 4*x^17 + x^15 + 3*x^13 + x^11))*y])),
 ([(2/(x^5 + 4*x))*y] d[x] + V(((x^32 - x^24 + 2*x^22 + x^18 + x^16 - x^14 + x^12 - 2*x^10 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^8*y - 2*x^4*y + y)) dx) + dV([((4*x^134 + 2*x^128 + 4*x^126 + x^124 + 4*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + x^112 + x^110 + 4*x^108 + 3*x^104 + 2*x^102 + 4*x^98 + 2*x^96 + x^94 + x^92 + 4*x^88 + x^84 + 3*x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 3*x^74 + x^70 + 4*x^68 + 3*x^66 + 2*x^64 + x^62 + 2*x^60 + 3*x^58 + 4*x^54 + 3*x^48 + 4*x^46 + 3*x^44 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 3*x^30 + 4*x^28 + 4*x^26 + x^22 + 3*x^18 + x^14 + 2*x^8 + 4*x^6 + 3*x^4)/(x^8 + 3*x^4 + 1))*y]), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y), [(3/(x^19 + 2*x^15 + 3*x^11 + x^9 + 4*x^7 + 4*x^5))*y] d[x] + V(((2*x^54 - x^52 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 + 2*x^40 - 2*x^36 - 2*x^32 - x^30 - 2*x^28 - 2*x^26 + x^22 + 2*x^20 + 2*x^18 + x^16 - x^14 + x^12 + x^10 + 2*x^8 - x^4 - 2*x^2 - 1)/(x^56*y + 2*x^52*y - 2*x^48*y - 2*x^46*y - x^44*y + 2*x^42*y + 2*x^36*y + x^32*y - 2*x^26*y - x^24*y + x^22*y - 2*x^20*y + x^18*y)) dx) + dV([((3*x^46 + 4*x^44 + x^42 + 2*x^40 + 3*x^38 + 4*x^34 + x^32 + x^28 + x^26 + 3*x^24 + 2*x^22 + 2*x^20 + 3*x^18 + 2*x^16 + 3*x^14 + 2*x^12 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^54 + 2*x^50 + 3*x^46 + 3*x^44 + 4*x^42 + 2*x^40 + 2*x^34 + x^30 + 3*x^24 + 4*x^22 + x^20 + 3*x^18 + x^16))*y])),
 ([((2*x^4 + 1)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^57 - 2*x^53 - 2*x^49 + x^47 - x^45 + x^43 - 2*x^41 - x^37 + 2*x^35 - 2*x^33 - x^31 + x^29 + 2*x^23 + x^21 + x^19 + x^17 - x^15 - x^13 - 2*x^11 + x^9 + x^7 + x^5 - 2*x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^139 + x^135 + 2*x^133 + 4*x^131 + x^129 + 2*x^125 + 2*x^119 + 2*x^113 + 2*x^111 + 2*x^109 + x^107 + 4*x^103 + x^101 + 3*x^93 + 2*x^91 + 3*x^89 + x^87 + 4*x^85 + 4*x^83 + 4*x^81 + 2*x^75 + 4*x^73 + x^71 + 4*x^69 + x^65 + x^63 + 2*x^61 + 2*x^59 + 4*x^57 + 3*x^55 + x^53 + 3*x^51 + 2*x^49 + 3*x^47 + x^45 + 4*x^43 + 2*x^39 + 2*x^37 + 2*x^35 + 2*x^31 + 3*x^25 + 2*x^23 + 4*x^21 + 3*x^19 + 4*x^15 + 4*x^13 + 4*x^11 + 4*x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^5*y] + V(((4*x^106 + 3*x^102 + 2*x^100 + x^98 + 3*x^94 + 4*x^92 + 3*x^90 + x^86 + 2*x^84 + 3*x^80 + 4*x^78 + 2*x^76 + x^72 + 2*x^68 + 2*x^66 + 4*x^64 + 4*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + 3*x^46 + x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + x^32 + 3*x^30 + x^24 + 3*x^22 + 2*x^20 + 2*x^18 + x^16 + x^12 + 3*x^8 + x^6 + 4)/x^5)*y), [((3*x^2 + 1)/(x^20 + 2*x^16 + 3*x^12 + x^10 + 4*x^8 + 4*x^6))*y] d[x] + V(((-x^60 + 2*x^56 - x^54 - x^52 - 2*x^50 + x^48 - 2*x^46 - x^44 + x^42 + x^40 - x^34 - 2*x^32 + x^30 - 2*x^24 - x^22 + x^20 - x^18 + 2*x^16 - 2*x^14 - x^12 + x^10 - 2*x^6 + x^4 + x^2 + 1)/(x^61*y + 2*x^57*y - 2*x^53*y - 2*x^51*y - x^49*y + 2*x^47*y + 2*x^41*y + x^37*y - 2*x^31*y - x^29*y + x^27*y - 2*x^25*y + x^23*y)) dx) + dV([((3*x^50 + 4*x^46 + x^44 + x^42 + x^40 + 2*x^38 + 4*x^36 + 2*x^34 + 4*x^32 + 4*x^30 + 4*x^28 + x^26 + 3*x^18 + 3*x^16 + x^14 + 3*x^12 + 2*x^10 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^59 + 2*x^55 + 3*x^51 + 3*x^49 + 4*x^47 + 2*x^45 + 2*x^39 + x^35 + 3*x^29 + 4*x^27 + x^25 + 3*x^23 + x^21))*y])),
 ([((3*x^7 + 3*x^3)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^52 - 2*x^48 + x^44 - 2*x^40 + x^38 - x^36 + x^30 - x^28 + 2*x^26 + x^24 + x^22 + x^20 - 2*x^18 + 2*x^16 + 2*x^14 + 2*x^12 - 2*x^10 - 2*x^8 + x^6 + x^4 + 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^154 + 4*x^150 + 3*x^148 + x^146 + 4*x^144 + 3*x^140 + x^134 + 2*x^130 + 2*x^128 + x^126 + 4*x^122 + 4*x^120 + x^118 + 4*x^116 + 4*x^110 + 4*x^108 + 3*x^106 + x^102 + 4*x^100 + 4*x^98 + 3*x^96 + x^90 + x^88 + 3*x^86 + 3*x^84 + x^82 + 3*x^80 + 3*x^78 + 3*x^74 + x^72 + 2*x^70 + 2*x^68 + 2*x^66 + 4*x^62 + 4*x^60 + x^58 + 3*x^56 + 2*x^54 + x^52 + 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^40 + x^38 + 2*x^36 + 4*x^34 + 2*x^30 + 2*x^28 + 2*x^26 + 2*x^24)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^6*y] + V(((x^120 + 2*x^116 + 3*x^114 + 4*x^112 + 2*x^108 + x^106 + 2*x^104 + 2*x^100 + 3*x^98 + x^96 + x^94 + 3*x^92 + 3*x^90 + x^88 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^76 + x^74 + x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 2*x^60 + 4*x^52 + x^50 + x^48 + 2*x^46 + 2*x^44 + x^40 + 3*x^38 + 4*x^34 + 2*x^32 + 3*x^30 + x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 3*x^16 + x^14 + 4*x^12 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + 2)/x^4)*y), [((2*x^2 + 4)/(x^19 + 4*x^17 + 3*x^15 + 2*x^13 + x^11 + 4*x^7))*y] d[x] + V(((-x^60 - 2*x^58 - 2*x^56 + x^54 - x^52 - x^50 + x^48 - x^46 + x^40 - 2*x^38 - 2*x^36 - x^30 - 2*x^28 + 2*x^24 + 2*x^22 + x^18 + x^14 - 2*x^12 + 2*x^10 - x^8 + 2*x^6 - x^4 - 2*x^2 + 1)/(x^62*y - x^60*y - 2*x^58*y + 2*x^56*y + x^54*y + 2*x^52*y + 2*x^50*y + 2*x^42*y - 2*x^40*y - 2*x^38*y + 2*x^36*y - 2*x^34*y - x^30*y + 2*x^28*y + x^26*y)) dx) + dV([((x^52 + x^46 + 2*x^44 + 2*x^42 + 3*x^40 + x^38 + 3*x^36 + x^34 + 3*x^30 + 3*x^28 + 3*x^26 + x^24 + 2*x^22 + 2*x^20 + 4*x^18 + 4*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + 3*x^8 + 2*x^6 + 3*x^4 + x^2 + 4)/(x^60 + 3*x^58 + 2*x^54 + 4*x^52 + 3*x^50 + 4*x^48 + x^46 + 4*x^44 + x^42 + x^40 + 2*x^38 + x^36 + x^34 + 2*x^32 + 3*x^30 + x^28 + x^26))*y])),
 ([(x^2/(x^10 + 3*x^6 + x^2 + 1))*y] d[x] + V(((-2*x^39 + 2*x^35 - 2*x^31 + 2*x^29 - x^27 + x^25 + 2*x^23 + x^19 - x^9 + 2*x^7 + 2*x^5 - x^3 - 2*x)/(x^30*y - x^26*y - 2*x^20*y - 2*x^16*y - 2*x^12*y + 2*x^10*y - 2*x^8*y - 2*x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^141 + 2*x^137 + x^135 + 4*x^133 + x^129 + 3*x^125 + 3*x^121 + x^117 + 2*x^115 + 2*x^113 + 3*x^111 + x^109 + 2*x^105 + 3*x^101 + 2*x^95 + 3*x^93 + 2*x^89 + 2*x^87 + 4*x^83 + 3*x^81 + x^79 + 4*x^77 + 4*x^73 + 4*x^71 + 3*x^69 + 2*x^67 + x^65 + 4*x^63 + 3*x^59 + 3*x^57 + 2*x^55 + 4*x^49 + x^47 + 4*x^43 + 3*x^41 + x^37 + 3*x^35 + 4*x^33 + 3*x^31 + 2*x^29 + 3*x^25 + 3*x^23 + x^21 + x^19)/(x^30 + 4*x^26 + 3*x^20 + 3*x^16 + 3*x^12 + 2*x^10 + 3*x^8 + 3*x^4 + 3*x^2 + 1))*y]), [2/x^7*y] + V(((2*x^118 + 4*x^114 + x^112 + 3*x^110 + 4*x^106 + 2*x^104 + 4*x^102 + x^96 + 4*x^94 + x^88 + 4*x^86 + 4*x^82 + x^80 + 3*x^78 + 3*x^76 + 4*x^70 + 2*x^62 + 4*x^60 + 4*x^58 + 2*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + x^46 + 4*x^42 + 4*x^38 + 4*x^36 + x^34 + 2*x^30 + 4*x^28 + 4*x^26 + 4*x^22 + 4*x^20 + 2*x^18 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 3*x^2 + 2)/x^7)*y), [((x^6 + 4*x^4 + 4*x^2 + 2)/(x^22 + 2*x^18 + 3*x^14 + x^12 + 4*x^10 + 4*x^8))*y] d[x] + V(((x^70 + 2*x^68 - x^66 - 2*x^64 - x^62 - 2*x^60 + x^56 + 2*x^54 - x^52 - 2*x^50 - x^48 - 2*x^46 + 2*x^44 - 2*x^42 + x^40 - x^38 - 2*x^36 - x^34 - 2*x^32 + x^30 + x^28 + x^26 - 2*x^24 + 2*x^20 + x^14 + 2*x^12 + x^10 - x^8 + x^6 - x^4 - x^2 + 2)/(x^71*y + 2*x^67*y - 2*x^63*y - 2*x^61*y - x^59*y + 2*x^57*y + 2*x^51*y + x^47*y - 2*x^41*y - x^39*y + x^37*y - 2*x^35*y + x^33*y)) dx) + dV([((x^60 + 2*x^56 + 4*x^54 + 4*x^52 + 2*x^50 + 3*x^46 + 2*x^44 + 4*x^40 + 3*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + 4*x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 2*x^16 + x^14 + 3*x^12 + 2*x^10 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^69 + 2*x^65 + 3*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + 2*x^49 + x^45 + 3*x^39 + 4*x^37 + x^35 + 3*x^33 + x^31))*y]))]
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[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(2):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for b in B:

....: [?7h[?12l[?25h[?25l[?7lprint("a")[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(b.regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in B:

....:     print(b.regular_form())

....: 

[?7h[?12l[?25h[?2004l( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V((0) dy) + dV((x^16 + 2*x^14 + x^12 + 2*x^6 + 4*x^4 + 2*x^2)*y), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V((0) dy) + dV((3*x^21 + x^19 + 3*x^17)*y), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.nth_root(3)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: bor b in B1:

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: 

....: [?7h[?12l[?25h[?25l[?7lsage: bor b in B1:

....: 

....: 

[?7h[?12l[?25h[?2004l  Input In [38]
    bor b in B1:
        ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7lsage: for b in B:

....:     print(b.regular_form())[?7h[?12l[?25h[?25l[?7lbor1:

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7lfor:

....:     print(b.regular_form())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1:[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(b.regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in B1:

....:     print(b.regular_form())

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [39], in <cell line: 1>()
      1 for b in B1:
----> 2     print(b.regular_form())

File <string>:90, in regular_drw_cech(cocycle)

File <string>:83, in regular_drw_form(omega)

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7l =F(2)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B1[0].omega0.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 B1[Integer(0)].omega0.regular_form()

File <string>:83, in regular_drw_form(omega)

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laB1[0][?7h[?12l[?25h[?25l[?7luB1[0][?7h[?12l[?25h[?25l[?7ltB1[0][?7h[?12l[?25h[?25l[?7loB1[0][?7h[?12l[?25h[?25l[?7lmB1[0][?7h[?12l[?25h[?25l[?7l(B1[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(B1[0]).coordinates()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:60, in __mul__(self, other)

File <string>:14, in __init__(self, C, g)

File <string>:253, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1002 try:
-> 1003     return self(str(element))
   1004 except TypeError:

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2689 """
-> 2690 return self._repr()
   2691 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
    337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
--> 338     return repr(self.numer())
    339 else:

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2689 """
-> 2690 return self._repr()
   2691 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [41], in <cell line: 1>()
----> 1 autom(B1[Integer(0)]).coordinates()

File <string>:97, in coordinates(self, basis, prec)

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:25, in de_rham_witt_lift(cech_class, prec)

File <string>:15, in de_rham_witt_lift_form8(omega)

File <string>:90, in diffn(self, dy_w)

File <string>:99, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

    [... skipping similar frames: __rmul__ at line 55 (4 times), sage.rings.integer.Integer.__mul__ at line 1964 (3 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times)]

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B1[0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B1[0]).coordinates(basis = B1)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 autom(B1[Integer(0)]).coordinates(basis = B1)

File <string>:26, in autom(self)

File <string>:23, in autom(self)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:82, in __pow__(self, exp)

File <string>:14, in __init__(self, C, g)

File <string>:253, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:482, in sage.rings.fraction_field_element.FractionFieldElement._repr_()
    480 if self.is_zero():
    481     return "0"
--> 482 s = "%s" % self.__numerator
    483 if self.__denominator != 1:
    484     denom_string = str( self.__denominator )

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2667, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2665         else:
   2666             var = ""
-> 2667         s += "%s%s"%(x,var)
   2668 s = s.replace(" + -", " - ")
   2669 s = re.sub(r' 1(\.0+)?\*',' ', s)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[0].regulr_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loB[0].omega0[?7h[?12l[?25h[?25l[?7lmB[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l=B[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lO = B[0].omega0[?7h[?12l[?25h[?25l[?7lM = B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM = B[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
0

....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - 
C

....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lO

 

 [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = OM.r()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lOM = B[0].omega0[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lO)[?7h[?12l[?25h[?25l[?7lM)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(OM)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 OM - de_rham_witt_lift_form0(OM)

File <string>:4, in de_rham_witt_lift_form0(omega)

File <string>:80, in regular_drw_form(omega)

File <string>:99, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:82, in __pow__(self, exp)

File <string>:14, in __init__(self, C, g)

File <string>:261, in reduction(C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2321, in sage.rings.polynomial.polynomial_element.Polynomial.__truediv__()
   2319 # Same parents => bypass coercion
   2320 if have_same_parent(left, right):
-> 2321     return (<Element>left)._div_(right)
   2322 
   2323 # Try division of polynomial by a scalar

File /ext/sage/9.7/src/sage/structure/element.pyx:2739, in sage.structure.element.RingElement._div_()
   2737     except AttributeError:
   2738         raise bin_op_exception('/', self, other)
-> 2739     return frac(self, other)
   2740 
   2741 def __divmod__(self, other):

File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__()
    897         return mor._call_(x)
    898     else:
--> 899         return mor._call_with_args(x, args, kwds)
    900 
    901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {}))

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:173, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
    171 else:
    172     if len(kwds) == 0:
--> 173         return C._element_constructor(x, *args)
    174     else:
    175         return C._element_constructor(x, *args, **kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field.py:648, in FractionField_generic._element_constructor_(self, x, y, coerce)
    646     x, y = x.numerator() * y.denominator(), y.numerator() * x.denominator()
    647 try:
--> 648     return self._element_class(self, x, y, coerce=coerce)
    649 except (TypeError, ValueError):
    650     pass

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(OM)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(om)

[?7h[?12l[?25h[?2004l[?7hV(((x^18 - x^16 + 2*x^14 + 2*x^12 + x^8 - 2*x^6 + 2*x^4 + 2*x^2 + 2)/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: OM.regular_form()

[?7h[?12l[?25h[?2004l[?7h[3*x*y] d[x] + [3*x^2 + 2] d[y] + V((0) dy) + dV((x^16 + 2*x^14 + x^12 + 2*x^6 + 4*x^4 + 2*x^2)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM.regular_form()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l=B[0].oega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l1[0].omega0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: OM = B1[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM = B1[0].omega0[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: OM.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 OM.regular_form()

File <string>:83, in regular_drw_form(omega)

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM.regular_form()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: OM

[?7h[?12l[?25h[?2004l[?7h[(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = OM.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lOM.r()[?7h[?12l[?25h[?25l[?7lsage: om = OM.r()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = B1[0].omega0[?7h[?12l[?25h[?25l[?7l-de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(om)

[?7h[?12l[?25h[?2004l[?7hV(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....:     C = omega.curve

....:     omega_aux = omega.r()

....:     omega_aux = omega_aux.regular_form()

....:     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....: ^Iprint('aux', aux)

....:     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....: ^Iprint('aux.omega, fct', aux.omega, fct)

....:     aux.h2 += fct^p

....: ^Iprint(aux.h2)

....:     aux.h2 = decomposition_g0_p2th_power(aux.h2)[0]

....:     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....:     return result[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....:     C = omega.curve

....:     omega_aux = omega.r()

....:     omega_aux = omega_aux.regular_form()

....:     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....: ^Iprint('aux', aux)

....:     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....: ^Iprint('aux.omega, fct', aux.omega, fct)

....:     aux.h2 += fct^p

....: ^Iprint(aux.h2)

....:     aux.h2 = decomposition_g0_p2th_power(aux.h2)[0]

....:     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....:     return result

[?7h[?12l[?25h[?2004l  Input In [53]
    print('aux', aux)
    ^
TabError: inconsistent use of tabs and spaces in indentation

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....: ^IC = omega.curve

....: ^Iomega_aux = omega.r()

....: ^Iomega_aux = omega_aux.regular_form()

....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....: ^Iprint('aux', aux)

....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....: ^Iprint('aux.omega, fct', aux.omega, fct)

....: ^Iaux.h2 += fct^p

....: ^Iprint(aux.h2)

....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0]

....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l....: ^Ireturn result

....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....: ^IC = omega.curve

....: ^Iomega_aux = omega.r()

....: ^Iomega_aux = omega_aux.regular_form()

....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....: ^Iprint('aux', aux)

....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....: ^Iprint('aux.omega, fct', aux.omega, fct)

....: ^Iaux.h2 += fct^p

....: ^Iprint(aux.h2)

....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0]

....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lraise ValueError("Test")[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(OM)

[?7h[?12l[?25h[?2004laux V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
aux.omega, fct ((-2*x^790 + x^786 - x^782 + 2*x^780 + 2*x^778 - 2*x^776 + 2*x^774 - x^770 + x^766 + x^764 - 2*x^762 + 2*x^760 + x^756 + x^754 + x^752 + 2*x^744 - x^740 + x^736 - 2*x^732 - x^724 - x^720 - x^716 + x^714 - x^712 + 2*x^710 - x^708 - 2*x^706 - x^704 + x^702 + 2*x^700 - 2*x^698 + 2*x^696 - 2*x^694 + x^692 + 2*x^690 + 2*x^688 + 2*x^686 - 2*x^684 - x^682 - x^680 - x^678 - 2*x^676 - 2*x^672 + 2*x^666 + 2*x^664 - 2*x^662 - 2*x^660 - x^658 + 2*x^656 - 2*x^654 - x^646 - 2*x^644 + 2*x^640 + x^638 + 2*x^636 - 2*x^634 + x^632 - 2*x^630 - 2*x^628 + x^626 + x^624 - x^622 + x^620 + 2*x^616 - x^614 + x^612 - x^606 - 2*x^604 - 2*x^602 - 2*x^598 - 2*x^596 + x^594 - x^592 - x^590 + 2*x^588 - x^586 - 2*x^584 - 2*x^582 - x^576 - x^574 - x^572 - 2*x^570 - 2*x^568 + 2*x^566 - 2*x^564 + 2*x^558 - 2*x^556 + 2*x^552 + x^548 - x^546 + x^544 + x^542 - 2*x^540 - x^538 + 2*x^536 - 2*x^534 + x^530 - 2*x^528 + x^526 - x^524 - x^522 - 2*x^516 + x^512 + x^510 + x^508 + x^502 + 2*x^498 + x^496 - 2*x^494 - x^492 - x^490 - x^488 + x^486 + x^484 - 2*x^482 + 2*x^480 - 2*x^476 + x^474 + x^470 + x^468 + 2*x^466 - 2*x^464 - x^462 + x^460 - 2*x^458 - 2*x^456 - 2*x^454 - x^452 - x^450 - x^448 + 2*x^446 - x^444 - 2*x^442 + 2*x^438 + 2*x^436 + 2*x^434 - 2*x^430 + x^428 + x^426 + x^424 - 2*x^422 + x^418 - 2*x^416 + x^414 - x^410 - 2*x^408 + x^406 + x^404 - x^402 + 2*x^398 - x^396 + x^392 - x^390 + x^388 + x^386 + x^384 + 2*x^380 + x^378 + 2*x^376 + 2*x^372 + 2*x^370 + x^368 - x^366 - 2*x^362 + 2*x^358 + 2*x^356 - x^352 + x^350 - 2*x^348 + x^346 + x^344 - 2*x^342 - 2*x^340 + 2*x^336 - x^334 + x^332 + 2*x^330 - 2*x^328 - 2*x^326 - 2*x^324 + 2*x^318 - 2*x^314 + 2*x^310 - x^308 + x^306 + x^302 + 2*x^298 + 2*x^296 + x^294 + x^292 - 2*x^290 - x^288 - x^286 - x^284 + x^282 + 2*x^280 + x^278 - x^276 + 2*x^274 + x^272 + 2*x^270 - x^266 + 2*x^264 + x^262 - x^260 - 2*x^258 + 2*x^256 - 2*x^254 + 2*x^252 + x^250 + x^246 - 2*x^244 + x^242 - 2*x^240 - 2*x^236 - x^232 - x^224 + 2*x^222 + x^220 + x^218 + x^216 - x^214 + 2*x^212 + 2*x^210 + 2*x^208 + 2*x^206 + 2*x^204 + 2*x^200 + x^198 + 2*x^196 + x^194 + 2*x^192 - 2*x^188 + 2*x^186 - 2*x^180 + 2*x^178 + x^174 - 2*x^172 + x^170 - x^168 - x^166 + 2*x^164 + 2*x^160 - x^158 + x^156 - x^154 - 2*x^152 - 2*x^150 - x^148 - x^144 - 2*x^140 + 2*x^138 + 2*x^134 + 2*x^132 - 2*x^130 + x^128 - x^126 + x^122 + 2*x^116 + x^114 - x^112 - x^108 - x^106 - x^104 + x^102 - 2*x^100 + x^96 - x^94 - 2*x^92 + 2*x^90 - x^88 - x^86 + x^82 + 2*x^80 - x^78 + 2*x^74 - x^72 + x^70 - 2*x^68 + 2*x^66 + 2*x^64 - 2*x^62 - 2*x^60 + 2*x^58 - 2*x^56 + 2*x^54 - 2*x^50 + 2*x^48 - x^46 + x^42 - 2*x^40 + 2*x^38 + 2*x^36 + x^34 + 2*x^32 - x^30 - x^26 - x^24 - 2*x^22 - x^20 - 2*x^18 + x^12)/y) dx ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 regular_drw_form(OM)

Input In [54], in regular_drw_form(omega)
      9 aux.h2 += fct**p
     10 print(aux.h2)
---> 11 aux.h2 = decomposition_g0_p2th_power(aux.h2)[Integer(0)]
     12 result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
     13 return result

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....: ^IC = omega.curve

....: ^Iomega_aux = omega.r()

....: ^Iomega_aux = omega_aux.regular_form()

....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....: ^Iprint('aux', aux)

....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....: ^Iprint('aux.omega, fct', aux.omega, fct)

....: ^Iaux.h2 += fct^p

....: ^Iprint('\n aux.h2', aux.h2, '\n')

....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0]

....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l....: ^Ireturn result

....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....: ^IC = omega.curve

....: ^Iomega_aux = omega.r()

....: ^Iomega_aux = omega_aux.regular_form()

....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....: ^Iprint('aux', aux)

....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....: ^Iprint('aux.omega, fct', aux.omega, fct)

....: ^Iaux.h2 += fct^p

....: ^Iprint('\n aux.h2', aux.h2, '\n')

....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0]

....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....: ^IC = omega.curve

....: ^Iomega_aux = omega.r()

....: ^Iomega_aux = omega_aux.regular_form()

....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....: ^Iprint('aux', aux)

....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....: ^Iprint('aux.omega, fct', aux.omega, fct)

....: ^Iaux.h2 += fct^p

....: ^Iprint('\n aux.h2', aux.h2, '\n')

....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0]

....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(OM)

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(OM)

[?7h[?12l[?25h[?2004laux V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
aux.omega, fct ((-2*x^790 + x^786 - x^782 + 2*x^780 + 2*x^778 - 2*x^776 + 2*x^774 - x^770 + x^766 + x^764 - 2*x^762 + 2*x^760 + x^756 + x^754 + x^752 + 2*x^744 - x^740 + x^736 - 2*x^732 - x^724 - x^720 - x^716 + x^714 - x^712 + 2*x^710 - x^708 - 2*x^706 - x^704 + x^702 + 2*x^700 - 2*x^698 + 2*x^696 - 2*x^694 + x^692 + 2*x^690 + 2*x^688 + 2*x^686 - 2*x^684 - x^682 - x^680 - x^678 - 2*x^676 - 2*x^672 + 2*x^666 + 2*x^664 - 2*x^662 - 2*x^660 - x^658 + 2*x^656 - 2*x^654 - x^646 - 2*x^644 + 2*x^640 + x^638 + 2*x^636 - 2*x^634 + x^632 - 2*x^630 - 2*x^628 + x^626 + x^624 - x^622 + x^620 + 2*x^616 - x^614 + x^612 - x^606 - 2*x^604 - 2*x^602 - 2*x^598 - 2*x^596 + x^594 - x^592 - x^590 + 2*x^588 - x^586 - 2*x^584 - 2*x^582 - x^576 - x^574 - x^572 - 2*x^570 - 2*x^568 + 2*x^566 - 2*x^564 + 2*x^558 - 2*x^556 + 2*x^552 + x^548 - x^546 + x^544 + x^542 - 2*x^540 - x^538 + 2*x^536 - 2*x^534 + x^530 - 2*x^528 + x^526 - x^524 - x^522 - 2*x^516 + x^512 + x^510 + x^508 + x^502 + 2*x^498 + x^496 - 2*x^494 - x^492 - x^490 - x^488 + x^486 + x^484 - 2*x^482 + 2*x^480 - 2*x^476 + x^474 + x^470 + x^468 + 2*x^466 - 2*x^464 - x^462 + x^460 - 2*x^458 - 2*x^456 - 2*x^454 - x^452 - x^450 - x^448 + 2*x^446 - x^444 - 2*x^442 + 2*x^438 + 2*x^436 + 2*x^434 - 2*x^430 + x^428 + x^426 + x^424 - 2*x^422 + x^418 - 2*x^416 + x^414 - x^410 - 2*x^408 + x^406 + x^404 - x^402 + 2*x^398 - x^396 + x^392 - x^390 + x^388 + x^386 + x^384 + 2*x^380 + x^378 + 2*x^376 + 2*x^372 + 2*x^370 + x^368 - x^366 - 2*x^362 + 2*x^358 + 2*x^356 - x^352 + x^350 - 2*x^348 + x^346 + x^344 - 2*x^342 - 2*x^340 + 2*x^336 - x^334 + x^332 + 2*x^330 - 2*x^328 - 2*x^326 - 2*x^324 + 2*x^318 - 2*x^314 + 2*x^310 - x^308 + x^306 + x^302 + 2*x^298 + 2*x^296 + x^294 + x^292 - 2*x^290 - x^288 - x^286 - x^284 + x^282 + 2*x^280 + x^278 - x^276 + 2*x^274 + x^272 + 2*x^270 - x^266 + 2*x^264 + x^262 - x^260 - 2*x^258 + 2*x^256 - 2*x^254 + 2*x^252 + x^250 + x^246 - 2*x^244 + x^242 - 2*x^240 - 2*x^236 - x^232 - x^224 + 2*x^222 + x^220 + x^218 + x^216 - x^214 + 2*x^212 + 2*x^210 + 2*x^208 + 2*x^206 + 2*x^204 + 2*x^200 + x^198 + 2*x^196 + x^194 + 2*x^192 - 2*x^188 + 2*x^186 - 2*x^180 + 2*x^178 + x^174 - 2*x^172 + x^170 - x^168 - x^166 + 2*x^164 + 2*x^160 - x^158 + x^156 - x^154 - 2*x^152 - 2*x^150 - x^148 - x^144 - 2*x^140 + 2*x^138 + 2*x^134 + 2*x^132 - 2*x^130 + x^128 - x^126 + x^122 + 2*x^116 + x^114 - x^112 - x^108 - x^106 - x^104 + x^102 - 2*x^100 + x^96 - x^94 - 2*x^92 + 2*x^90 - x^88 - x^86 + x^82 + 2*x^80 - x^78 + 2*x^74 - x^72 + x^70 - 2*x^68 + 2*x^66 + 2*x^64 - 2*x^62 - 2*x^60 + 2*x^58 - 2*x^56 + 2*x^54 - 2*x^50 + 2*x^48 - x^46 + x^42 - 2*x^40 + 2*x^38 + 2*x^36 + x^34 + 2*x^32 - x^30 - x^26 - x^24 - 2*x^22 - x^20 - 2*x^18 + x^12)/y) dx ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y

 aux.h2 ((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y 

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 regular_drw_form(OM)

Input In [56], in regular_drw_form(omega)
      9 aux.h2 += fct**p
     10 print('\n aux.h2', aux.h2, '\n')
---> 11 aux.h2 = decomposition_g0_p2th_power(aux.h2)[Integer(0)]
     12 result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
     13 return result

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C1.x^7
6

....: 6 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2*C1.x
^

....: 714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^664 + 
2

....: *C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1.x^61
2

....:  + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + 3*C
1

....: .x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^506 + 3
*

....: C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2*C1.x
^

....: 444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 + C1
.

....: x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x^332 
+

....:  3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^292 + C
1

....: .x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.x^226

....: + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 + 3*
C

....: 1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1.x^12
4

....:  + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + 2*C1
.

....: x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4*C1.
x

....: ^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + 3*C1
.

....: x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1.x^11
8

....:  + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C1.x^8
8

....:  + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^58 + 3
*

....: C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + 2*C1
.

....: x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7lsage: ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C1.x^7
6

....: 6 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2*C1.x
^

....: 714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^664 + 
2

....: *C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1.x^61
2

....:  + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + 3*C
1

....: .x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^506 + 3
*

....: C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2*C1.x
^

....: 444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 + C1
.

....: x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x^332 
+

....:  3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^292 + C
1

....: .x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.x^226

....: + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 + 3*
C

....: 1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1.x^12
4

....:  + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + 2*C1
.

....: x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4*C1.
x

....: ^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + 3*C1
.

....: x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1.x^11
8

....:  + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C1.x^8
8

....:  + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^58 + 3
*

....: C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + 2*C1
.

....: x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y

[?7h[?12l[?25h[?2004l[?7h((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C1.x^7
6

....: 6 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2*C1.x
^

....: 714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^664 + 
2

....: *C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1.x^61
2

....:  + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 + 3*C
1

....: .x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^506 + 3
*

....: C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2*C1.x
^

....: 444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 + C1
.

....: x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x^332 
+

....:  3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^292 + C
1

....: .x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.x^226

....: + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166 + 3*
C

....: 1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1.x^12
4

....:  + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 + 2*C1
.

....: x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 4*C1.
x

....: ^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 + 3*C1
.

....: x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1.x^11
8

....:  + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C1.x^8
8

....:  + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^58 + 3
*

....: C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 + 2*C1
.

....: x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lfor b in B1:[?7h[?12l[?25h[?25l[?7l1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C
1

....: .x^766 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2
*

....: C1.x^714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^6
6

....: 4 + 2*C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1
.

....: x^612 + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 
+

....:  3*C1.x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^50
6

....:  + 3*C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2
*

....: C1.x^444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374

....: + C1.x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x
^

....: 332 + 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^29
2

....:  + C1.x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.
x

....: ^226 + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166

....: + 3*C1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1
.

....: x^124 + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 +

....: 2*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 
4

....: *C1.x^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 +

....: 3*C1.x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1
.

....: x^118 + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C
1

....: .x^88 + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^5
8

....:  + 3*C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 +

....: 2*C1.x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7lsage: f1 = ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C
1

....: .x^766 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2
*

....: C1.x^714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^6
6

....: 4 + 2*C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1
.

....: x^612 + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 
+

....:  3*C1.x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^50
6

....:  + 3*C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2
*

....: C1.x^444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374

....: + C1.x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x
^

....: 332 + 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^29
2

....:  + C1.x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.
x

....: ^226 + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166

....: + 3*C1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1
.

....: x^124 + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 +

....: 2*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 
4

....: *C1.x^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 +

....: 3*C1.x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1
.

....: x^118 + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C
1

....: .x^88 + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^5
8

....:  + 3*C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 +

....: 2*C1.x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C
1

....: .x^766 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2
*

....: C1.x^714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C1.x^672 + 2*C1.x^666 + 4*C1.x^6
6

....: 4 + 2*C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1
.

....: x^612 + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^566 + 3*C1.x^564 + 4*C1.x^562 
+

....:  3*C1.x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C1.x^514 + C1.x^512 + 4*C1.x^50
6

....:  + 3*C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^454 + 4*C1.x^452 + C1.x^446 + 2
*

....: C1.x^444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374
 

....: + C1.x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*C1.x^336 + 3*C1.x^334 + 4*C1.x
^

....: 332 + 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^29
2

....:  + C1.x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.
x

....: ^226 + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166
 

....: + 3*C1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 + C1.x^132 + 2*C1.x^126 + 4*C1
.

....: x^124 + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 +
 

....: 2*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^26 + 3*C1.x^24 + 4*C1.x^22 + 
4

....: *C1.x^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 +
 

....: 3*C1.x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + C1.x^120 + 3*C1
.

....: x^118 + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C
1

....: .x^88 + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + C1.x^62 + 4*C1.x^60 + 3*C1.x^5
8

....:  + 3*C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 +
 

....: 2*C1.x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.coordinates()

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.diffn()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



































 [?7h[?12l[?25h[?25l[?7lf1.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.diffn().int()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 































 [?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(aux.h2)[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7lf)[0][?7h[?12l[?25h[?25l[?7l1)[0][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_p2th_power(f1)[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [62], in <cell line: 1>()
----> 1 decomposition_g0_p2th_power(f1)[Integer(0)]

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1.diffn().int()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2 = f1.pth_root()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(f1)[0][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_p2th_power(f1)[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l2)[0][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_p2th_power(f2)[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [64], in <cell line: 1>()
----> 1 decomposition_g0_p2th_power(f2)[Integer(0)]

File <string>:11, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2 = f1.pth_root()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2.diffn().int()

[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2.diffn().int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(f2)[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lth_power(f2)[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(f2)[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [67], in <cell line: 1>()
----> 1 decomposition_g0_pth_power(f2)[Integer(0)]

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0, A = decomposition_g0_pth_power(fct)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g0, A = decomposition_g0_pth_power(f1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0, A = decomposition_g0_pth_power(f1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: g0

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA0, A1 = decomposition_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7lsage: A0, A1 = decomposition_g0_pth_power(A)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [72], in <cell line: 1>()
----> 1 A0, A1 = decomposition_g0_pth_power(A)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA0, A1 = decomposition_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.leading_coefficient()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?7h((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = fct.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l.difn().regular_form()[?7h[?12l[?25h[?25l[?7l .difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega = A.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0 = omega.int()[?7h[?12l[?25h[?25l[?7lsage: g0 = omega.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [77], in <cell line: 1>()
----> 1 g0 = omega.int()

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = A.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [78], in <cell line: 1>()
----> 1 omega.int()

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega

[?7h[?12l[?25h[?2004l[?7h((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn 0*C.x

....: ^I#which = random.choice([0, 1])

....: ^IP = self.dx.function

....: ^IQ = self.dy.function

....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px

....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I    print('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn 0*C.x

....: ^I#which = random.choice([0, 1])

....: ^IP = self.dx.function

....: ^IQ = self.dy.function

....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px

....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I    print('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

[?7h[?12l[?25h[?2004l  Input In [80]
    W += Rx(numerator/f.derivative())
    ^
TabError: inconsistent use of tabs and spaces in indentation

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn 0*C.x

....: ^I#which = random.choice([0, 1])

....: ^IP = self.dx.function

....: ^IQ = self.dy.function

....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px

....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l#which = random.choice([0, 1])

P = self.dx.function

Qy

Py,Px = P.quo_rem(y) #P = y*Py + Px

QQQ

resultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

numerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Id = .degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^I#which = random.choice([0, 1])

....: ^IP = self.dx.function

....: ^IQ = self.dy.function

....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px

....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li, j = (x^6*y^7).exponents()[0][?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: int(omega)

[?7h[?12l[?25h[?2004lnumerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 int(omega)

Input In [81], in int(self)
     32 	if a < Integer(0):
     33 		print('numerator', numerator)
---> 34 		W += Rx(numerator/f.derivative())
     35 		numerator = Rx(Integer(0))
     36 result = result + superelliptic_function(C, y*W)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*x^10 + 2*x^6 + x^2 + 2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*x^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1x^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l.x^10 + 2*x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l.x^6 + x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + 2/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*/C1.y*C.dx[?7h[?12l[?25h[?25l[?7lC/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l1/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l./C1.y*C.dx[?7h[?12l[?25h[?25l[?7lo/C1.y*C.dx[?7h[?12l[?25h[?25l[?7ln/C1.y*C.dx[?7h[?12l[?25h[?25l[?7le/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l()/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1

[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.int()

[?7h[?12l[?25h[?2004l[?7h((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C1.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C1.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.int()

[?7h[?12l[?25h[?2004l[?7h((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l1 = suerelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.regular_form()

[?7h[?12l[?25h[?2004l[?7h((x^15 + 2*x^7 + x^5 + 2*x^3 + 4*x)*y) dx + (4*x^20 + x^16 + 3*x^12 + 3*x^6 + 2*x^4 + 2*x^2 + 1) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1

[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C1.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1 == 2*C1.y.diffn()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1 == 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l@[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1, 2*C1.diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [93], in <cell line: 1>()
----> 1 omega1, Integer(2)*C1.diffn()

AttributeError: 'superelliptic' object has no attribute 'diffn'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1, 2*C1.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lydifn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1, 2*C1.y.diffn()

[?7h[?12l[?25h[?2004l[?7h(((2*x^10 + 2*x^6 + x^2 + 2)/y) dx, ((2*x^10 + x^6 + 2*x^2 - 1)/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C1.dx[?7h[?12l[?25h[?25l[?7l()C1.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(C[?7h[?12l[?25h[?25l[?7l1C1.dx[?7h[?12l[?25h[?25l[?7l.C1.dx[?7h[?12l[?25h[?25l[?7lyC1.dx[?7h[?12l[?25h[?25l[?7l()C1.dx[?7h[?12l[?25h[?25l[?7l()^C1.dx[?7h[?12l[?25h[?25l[?7l(C1.dx[?7h[?12l[?25h[?25l[?7l-C1.dx[?7h[?12l[?25h[?25l[?7l1C1.dx[?7h[?12l[?25h[?25l[?7l()C1.dx[?7h[?12l[?25h[?25l[?7l()*C1.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lu(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lx(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l=(C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = (C1.y)^(-1)*C1.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.omegacartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [96], in <cell line: 1>()
----> 1 aux.int()

File <string>:198, in int(self)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
   3992 cdef Py_ssize_t n
   3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
   3996 return S(p)

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
   2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
   2622 if right_inverse is None:
-> 2623     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
   2624 else:
   2625     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)

ZeroDivisionError: inverse of Mod(0, 5) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.int()[?7h[?12l[?25h[?25l[?7l = (C1.y)^(-1)*C1.dx[?7h[?12l[?25h[?25l[?7lomega1, 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 2*C1.y.difn()[?7h[?12l[?25h[?25l[?7l- 2*C1.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega1- 2*C1.y.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^6 - x^2 - 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1- 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(omega1- 2*C1.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (omega1- 2*C1.y.diffn()).int()

[?7h[?12l[?25h[?2004l[?7h((3*x^28 + 4*x^26 + 4*x^24 + x^22 + 4*x^20 + 4*x^16 + x^14 + 2*x^12 + 2*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 4)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1- 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega1.int()

[?7h[?12l[?25h[?2004l[?7h((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7l(omega1- 2*C1.y.diffn()).int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7leint()[?7h[?12l[?25h[?25l[?7lgint()[?7h[?12l[?25h[?25l[?7luint()[?7h[?12l[?25h[?25l[?7llint()[?7h[?12l[?25h[?25l[?7laint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7l_int()[?7h[?12l[?25h[?25l[?7lfint()[?7h[?12l[?25h[?25l[?7loint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7lmint()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (omega1- 2*C1.y.diffn()).regular_form.int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [100], in <cell line: 1>()
----> 1 (omega1- Integer(2)*C1.y.diffn()).regular_form.int()

AttributeError: 'function' object has no attribute 'int'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(omega1- 2*C1.y.diffn()).regular_form.int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.int()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (omega1- 2*C1.y.diffn()).regular_form().int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [101], in <cell line: 1>()
----> 1 (omega1- Integer(2)*C1.y.diffn()).regular_form().int()

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1

[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(omega)[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: int(omega)

[?7h[?12l[?25h[?2004lnumerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [104], in <cell line: 1>()
----> 1 int(omega)

Input In [81], in int(self)
     32 	if a < Integer(0):
     33 		print('numerator', numerator)
---> 34 		W += Rx(numerator/f.derivative())
     35 		numerator = Rx(Integer(0))
     36 result = result + superelliptic_function(C, y*W)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.polynomial.derivative()

[?7h[?12l[?25h[?2004l[?7h2*x^10 + x^6 + 2*x^2 + 4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1

[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B1[0].omega0.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [108], in <cell line: 1>()
----> 1 B1[Integer(0)].omega0.regular_form()

File <string>:83, in regular_drw_form(omega)

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=B1[0].omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB1[0].omega0[?7h[?12l[?25h[?25l[?7lsage: OM = B1[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM = B1[0].omega0[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: OM

[?7h[?12l[?25h[?2004l[?7h[(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = B1[0].omega0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l- de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lsage: OM - de_rham_witt_lift_form0(om)

[?7h[?12l[?25h[?2004l[?7hV(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laOM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7luOM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7lxOM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l OM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l=OM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l OM - de_rham_wit_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = OM - de_rham_witt_lift_form0(om)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lomega.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aom = aux.omega

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom = aux.omega[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: aom

[?7h[?12l[?25h[?2004l[?7h((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: aom.is_regular_on_U

 aom.is_regular_on_U0    

 aom.is_regular_on_Uinfty





 [?7h[?12l[?25h[?25l[?7l0

 aom.is_regular_on_U0    



 <unknown> [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aom.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7laom.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef int(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(f2)[0][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition

 decomposition               decomposition_g0_pth_power  decomposition_omega0_hpdh  

 decomposition_g0_g8         decomposition_g8_p2th_power decomposition_omega0_omega8

                    decomposition_g0_p2th_power decomposition_g8_pth_power  decomposition_omega8_hpdh  



 [?7h[?12l[?25h[?25l[?7l

 decomposition              





 <unknown> [?7h[?12l[?25h[?25l[?7l_g0_pth_power

 decomposition               decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7lomega0hpdh

 decomposition_g0_pth_power  decomposition_omega0_hpdh  [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lodecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lmdecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l0decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l,decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lhdecomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l=decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aom0, h = decomposition_omega0_hpdh(aom)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7laom0, h = decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm0, h = decomposition_omega0_hpdh(aom)[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmh.difn()[?7h[?12l[?25h[?25l[?7luh.difn()[?7h[?12l[?25h[?25l[?7llh.difn()[?7h[?12l[?25h[?25l[?7lth.difn()[?7h[?12l[?25h[?25l[?7l_h.difn()[?7h[?12l[?25h[?25l[?7lbh.difn()[?7h[?12l[?25h[?25l[?7lyh.difn()[?7h[?12l[?25h[?25l[?7l_h.difn()[?7h[?12l[?25h[?25l[?7lph.difn()[?7h[?12l[?25h[?25l[?7l(h.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: aom.verschiebung() == aom0.verschiebung() + mult_by_p(h.diffn())

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7laom.verschiebung() == aom0.verschiebung() + mult_by_p(h.diffn())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l()mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l(mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l()mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l(mult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7lmult_by_p(h.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(h.diffn()) == (0*C.dx).verschiebung()

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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(h.diffn()) == (0*C.dx).verschiebung()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt_by_p(h.diffn()) == (0*C.dx).verschiebung()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(h.diffn()) == (h^(p-1)*h.diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(h.diffn()) == (h^(p-1)*h.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(h.diffn()) == (h^p).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: h1 = h^p

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef int(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(f2)[0][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(f2)[0]

 decomposition               decomposition_g0_pth_power  decomposition_omega0_hpdh  

 decomposition_g0_g8         decomposition_g8_p2th_power decomposition_omega0_omega8

 decomposition_g0_p2th_power decomposition_g8_pth_power  decomposition_omega8_hpdh  



 [?7h[?12l[?25h[?25l[?7l

 decomposition              





 <unknown> [?7h[?12l[?25h[?25l[?7l_g0_pth_power

 decomposition               decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7l82th_power

 decomposition_g0_pth_power 

 decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l0th_power

 decomposition_g0_pth_power 

 decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l

 decomposition               decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7l_g0_g8

 decomposition              

 decomposition_g0_g8        [?7h[?12l[?25h[?25l[?7lp2th_power



 decomposition_g0_g8        

 decomposition_g0_p2th_power[?7h[?12l[?25h[?25l[?7l(f2)[0]







[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_p2th_power(h1)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [122], in <cell line: 1>()
----> 1 decomposition_g0_p2th_power(h1)

File <string>:12, in decomposition_g0_p2th_power(fct)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1 = h^p[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: h1

[?7h[?12l[?25h[?2004l[?7h((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1.diffn()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().form() == h1.diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1.diffn().regular_form().form() == h1.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().int()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_p2th_power(h1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_p2th_power(h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lth_power(h1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(h1)

[?7h[?12l[?25h[?2004l[?7h(0,
 ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAdecomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l1decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l,decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7lAdecomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l=decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, A = decomposition_g0_pth_power(h1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A = decomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l.diffn().regular_frm()[?7h[?12l[?25h[?25l[?7ldiffn().regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn()[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn().int()

[?7h[?12l[?25h[?2004l[?7h((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn().int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7leint()[?7h[?12l[?25h[?25l[?7lgint()[?7h[?12l[?25h[?25l[?7luint()[?7h[?12l[?25h[?25l[?7llint()[?7h[?12l[?25h[?25l[?7laint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7l_int()[?7h[?12l[?25h[?25l[?7lfint()[?7h[?12l[?25h[?25l[?7loint()[?7h[?12l[?25h[?25l[?7lrint()[?7h[?12l[?25h[?25l[?7lmint()[?7h[?12l[?25h[?25l[?7l(int()[?7h[?12l[?25h[?25l[?7l()int()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.diffn().regular_form().int()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [130], in <cell line: 1>()
----> 1 A.diffn().regular_form().int()

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lnA.difn().regular_form()[?7h[?12l[?25h[?25l[?7ltA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lint(A.difn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [131], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [81], in int(self)
     32 	if a < Integer(0):
     33 		print('numerator', numerator)
---> 34 		W += Rx(numerator/f.derivative())
     35 		numerator = Rx(Integer(0))
     36 result = result + superelliptic_function(C, y*W)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lintA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7lA.difn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.diffn().regular_form()

[?7h[?12l[?25h[?2004l[?7h((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IP = self.dx.function

....: ^IQ = self.dy.function

....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px

....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lQy

Py,Px = P.quo_rem(y) #P = y*Py + Px

QQQ

resultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

numerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^IQ = self.dy.function

....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px

....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
numerator:  x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
numerator:  4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
numerator:  2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
numerator:  3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
numerator:  4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
numerator:  x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
numerator:  x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
numerator:  3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
numerator:  2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
numerator:  x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
numerator:  4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
numerator:  4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
numerator:  2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
numerator:  2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
numerator:  3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
numerator:  4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
numerator:  4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
numerator:  4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
numerator:  3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
numerator:  4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38
numerator:  3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36
numerator:  2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34
numerator:  x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32
numerator:  3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26
numerator:  x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22
numerator:  3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18
numerator:  3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14
numerator:  x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12
numerator:  4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8
numerator:  3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6
numerator:  x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4
numerator:  2*x^10 + 2*x^6 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [134], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [133], in int(self)
     34 	if a < Integer(0):
     35 		print('numerator', numerator)
---> 36 		W += Rx(numerator/f.derivative())
     37 		numerator = Rx(Integer(0))
     38 result = result + superelliptic_function(C, y*W)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self == (C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

numerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/y)

print(self == (C.y*W1).diff() + n1)

d = numerator.degree(

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self == (C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self == (C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7lsage: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [136], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [135], in int(self)
     24 W1 = superelliptic_function(C, W)
     25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self == (C.y*W1).diffn() + n1)
     27 d = numerator.degree()
     28 r = f.degree()

File <string>:12, in __eq__(self, other)

AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 











 [?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

numerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/y)

print(self.form() == (C.y*W1).diffn() + n1)

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
False
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
False
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
False
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
False
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
numerator:  x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
False
numerator:  4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
False
numerator:  2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
False
numerator:  3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
False
numerator:  4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
False
numerator:  x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
False
numerator:  x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
False
numerator:  3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
False
numerator:  2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
False
numerator:  x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
False
numerator:  4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
False
numerator:  4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
False
numerator:  2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
False
numerator:  2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
False
numerator:  3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
False
numerator:  4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [138], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [137], in int(self)
     24 W1 = superelliptic_function(C, W)
     25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self.form() == (C.y*W1).diffn() + n1)
     27 d = numerator.degree()
     28 r = f.degree()

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File <string>:296, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

numerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/y)

print(self.form(), (C.y*W1).diffn() + n1)

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + x^136 + x^130 - 2*x^128 - x^126 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 + x^130 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 + 2*x^128 + 2*x^124 + 2*x^120 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + 2*x^120 + 2*x^118 - 2*x^116 - x^114 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 + x^118 - 2*x^116 - 2*x^114 - x^112 - x^110 + x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 - 2*x^116 - x^112 - x^110 - 2*x^108 - x^104 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 - 2*x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - 2*x^102 - 2*x^98 + 2*x^96 - 2*x^94 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + 2*x^98 + 2*x^96 + 2*x^94 - x^90 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + 2*x^96 - x^90 - 2*x^88 - x^86 - 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 - x^90 + 2*x^88 + x^86 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^86 - x^82 + 2*x^80 - x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^86 + x^84 - x^82 + 2*x^80 + x^76 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 - x^82 + 2*x^80 - 2*x^78 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + 2*x^80 + x^78 + x^74 + 2*x^72 - x^70 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + x^78 - x^76 + x^74 + 2*x^70 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + 2*x^70 - 2*x^68 - x^66 + x^64 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 - 2*x^68 + x^66 + x^64 - x^62 - 2*x^58 - 2*x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - x^62 + 2*x^58 - 2*x^54 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^58 + 2*x^54 + x^52 + 2*x^50 - x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 + x^58 - x^56 + 2*x^54 - x^52 - x^48 + 2*x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 - x^56 - x^52 + 2*x^48 + x^46 + 2*x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [140], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [139], in int(self)
     24 W1 = superelliptic_function(C, W)
     25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self.form(), (C.y*W1).diffn() + n1)
     27 d = numerator.degree()
     28 r = f.degree()

File <string>:17, in form(self)

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    986 try:
    987     if '/' in element:
--> 988         element = sage_eval(element,d)
    989     else:
    990         element = element.replace("^","**")

File /ext/sage/9.7/src/sage/misc/sage_eval.py:192, in sage_eval(source, locals, cmds, preparse)
    190 else:
    191     if preparse:
--> 192         source = preparser.preparse(source)
    194 if cmds:
    195     exec(cmd_seq, sage.all.__dict__, locals)

File /ext/sage/9.7/src/sage/repl/preparse.py:1816, in preparse(line, reset, do_time, ignore_prompts, numeric_literals)
   1811     L = implicit_mul(L, level = implicit_mul_level)
   1813 if numeric_literals:
   1814     # Wrapping
   1815     # 1 + 0.5 -> Integer(1) + RealNumber('0.5')
-> 1816     L = preparse_numeric_literals(L, quotes=quote_state.safe_delimiter())
   1818 # Generators
   1819 # R.0 -> R.gen(0)
   1820 L = re.sub(r'(\b[^\W\d]\w*|[)\]])\.(\d+)', r'\1.gen(\2)', L)

File /ext/sage/9.7/src/sage/repl/preparse.py:1286, in preparse_numeric_literals(code, extract, quotes)
   1283     all_num_regex = re.compile(all_num, re.I)
   1285 for m in all_num_regex.finditer(code):
-> 1286     start, end = m.start(), m.end()
   1287     num = m.group(1)
   1288     postfix = m.groups()[-1].upper()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

numerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/y)

print(self.form() == (2*.y*W1).diffn( + n1)

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7lsage: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
False
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
False
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
False
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
False
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
numerator:  x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
False
numerator:  4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
False
numerator:  2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
False
numerator:  3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
False
numerator:  4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
False
numerator:  x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
False
numerator:  x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
False
numerator:  3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
False
numerator:  2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
False
numerator:  x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [142], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [141], in int(self)
     23 print('W: ', W)
     24 W1 = superelliptic_function(C, W)
---> 25 n1 = superelliptic_form(C, numerator/y)
     26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1)
     27 d = numerator.degree()

File <string>:7, in __init__(self, C, g)

File <string>:296, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1007 try:
   1008     # now try calling the base ring's __call__ methods
-> 1009     element = self.base_ring()(element)
   1010     _p = p_NSet(sa2si(element,_ring), _ring)
   1011     return new_MP(self,_p)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1143 """
   1144 TESTS::
   1145 
   (...)
   1182     True
   1183 """
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):
   1187     raise TypeError("error coercing to finite field")

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199         return a
    200 t = modulus.element_class()
--> 201 return t(parent, value)
    202 
    203 

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    378 else:
    379     try:
--> 380         z = integer_ring.Z(value)
    381     except (TypeError, ValueError):
    382         from sage.structure.element import Expression

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:
    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    829     return R(self.__numerator)
    830 else:
--> 831     self.reduce()
    832     num = R(self.__numerator)
    833     inv_den = R(self.__denominator).inverse_of_unit()

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
   1237 if self._is_reduced:
   1238     return
-> 1239 super(self.__class__, self).reduce()
   1240 self.normalize_leading_coefficients()
   1241 

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    162     return codomain.coerce(nnum/nden)
    163 
--> 164 cpdef reduce(self):
    165     """
    166     Reduce this fraction.

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    195     return
    196 try:
--> 197     g = self.__numerator.gcd(self.__denominator)
    198     if not g.is_unit():
    199         self.__numerator //= g

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4911         raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
   4912     else:
-> 4913         return doit(self, other)
   4914 
   4915 @coerce_binop

File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
    944 f1 = Num(f.numerator())
    945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4906, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4904 tgt = flatten.codomain()
   4905 if tgt.ngens() > 1 and tgt._has_singular:
-> 4906     g = flatten(self).gcd(flatten(other))
   4907     return flatten.section()(g)
   4908 try:

File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
    767 if P is D: # we certainly want to call _call_/with_args
    768     if not args and not kwds:
--> 769         return self._call_(x)
    770     return self._call_with_args(x, args, kwds)
    771 # Is there coercion?

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:220, in FlatteningMorphism._call_(self, p)
    218     for mon, pp in p.items():
    219         assert pp.parent() is ring
--> 220         for i, j in pp.dict().items():
    221             new_p[(i,)+(mon)] = j
    222 elif is_MPolynomialRing(ring):

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result)

....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/y)

print(self.form() == (2*.y*W1).diffn( + n1 + result)

, (2*C.y*W1).diffn() +n1 +result)

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result)

....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result)

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [144], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [143], in int(self)
     24 W1 = superelliptic_function(C, W)
     25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1 + result)
     27 print(self.form(), (Integer(2)*C.y*W1).diffn() + n1 + result)
     28 d = numerator.degree()

File <string>:19, in __add__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/y)

print(self.form() == (2*.y*W1).diffn( + n1 + result.diffn())

, (2*C.y*W1).diffn() +n1 +result.diffn())

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7lsage: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lregular_drw_form(OM)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
False
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [146], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [145], in int(self)
     25 n1 = superelliptic_form(C, numerator/y)
     26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1 + result.diffn())
---> 27 print(self.form(), (Integer(2)*C.y*W1).diffn() + n1 + result.diffn())
     28 d = numerator.degree()
     29 r = f.degree()

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File <string>:282, in reduction_form(C, g)

File <string>:263, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:974, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    972 if isinstance(element, (SingularElement, cypari2.gen.Gen)):
    973     element = str(element)
--> 974 elif is_Macaulay2Element(element):
    975     element = element.external_string()
    976 

File /ext/sage/9.7/src/sage/interfaces/macaulay2.py:1835, in is_Macaulay2Element(x)
   1823         """
   1824         EXAMPLES::
   1825 
   (...)
   1828             -- code for method: resolution(Matrix)...
   1829         """
   1830         return self._obj.parent().eval(
   1831             'code select(methods %s, m->instance(%s, m#1))'
   1832             % (self._name, self._obj._name))
-> 1835 def is_Macaulay2Element(x):
   1836     """
   1837     EXAMPLES::
   1838 
   (...)
   1843         True
   1844     """
   1845     return isinstance(x, Macaulay2Element)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/y)

print(self.form() == (C.y*W1).diffn() + n1 + result.diffn())

, (C.y*W1).diffn() +n1 +result.diffn())

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/y)

....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lsage: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + x^136 + x^130 - 2*x^128 - x^126 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 + x^130 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 + 2*x^128 + 2*x^124 + 2*x^120 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Input In [148], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [147], in int(self)
     25 n1 = superelliptic_form(C, numerator/y)
     26 print(self.form() == (C.y*W1).diffn() + n1 + result.diffn())
---> 27 print(self.form(), (C.y*W1).diffn() + n1 + result.diffn())
     28 d = numerator.degree()
     29 r = f.degree()

File <string>:17, in form(self)

File <string>:65, in __mul__(self, other)

File <string>:7, in __init__(self, C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    986 try:
    987     if '/' in element:
--> 988         element = sage_eval(element,d)
    989     else:
    990         element = element.replace("^","**")

File /ext/sage/9.7/src/sage/misc/sage_eval.py:186, in sage_eval(source, locals, cmds, preparse)
    183     locals = {}
    185 import sage.all
--> 186 if cmds:
    187     cmd_seq = cmds + '\n_sage_eval_returnval_ = ' + source
    188     if preparse:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/(2*y))

....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lnumerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/(2*y))

print(self.form() == (C.y*W1).diffn() + n1 + result.diffn())

, (C.y*W1).diffn() +n1 +result.diffn())

d = numerator.degree()

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/(2*y))

....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator:  2*x^10 + 2*x^6 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [150], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [149], in int(self)
     38 	if a < Integer(0):
     39 		print('numerator', numerator)
---> 40 		W += Rx(numerator/f.derivative())
     41 		numerator = Rx(Integer(0))
     42 result = result + superelliptic_function(C, y*W)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: ^IQy, Qx = Q.quo_rem(y)

....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/(2*y))

....: ^I^Iprint((C.y*W1).diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result[?7h[?12l[?25h[?25l[?7lresultsuperelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

numerator = Rx(2*f*Py + f.derivative()*Qx)

# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

W = Rx(0)

while(numerator != 0):

^Iprint('numerator: ', numerator)

W: ', W)

W1 = superelliptic_function(C, W)

norm(C, numerator/(2*y))

print((C.y*W1).dffn())

d = numerator.degree

rf.dgree()

n_lead = numerator.leading_coefficient()

fRx(f).leading_coefficient()

a = d - (r-1)

if a >=0:

^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

 += W_coeff*Rx(x^a)

numerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

= Rx(numerator)

if a < 0:

^Iprint('numerator', numerator)

W += Rx(numerator/f.derivative())

numerator = Rx(0)

result = result+ superelliptic_function(C, y*W)

returnresult

[?7h[?12l[?25h[?25l[?7l....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())

....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)

....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.

....: ^IW = Rx(0)

....: ^Iwhile(numerator != 0):

....: ^I^Iprint('numerator: ', numerator)

....: ^I^Iprint('W: ', W)

....: ^I^IW1 = superelliptic_function(C, W)

....: ^I^In1 = superelliptic_form(C, numerator/(2*y))

....: ^I^Iprint((C.y*W1).diffn())

....: ^I^Id = numerator.degree()

....: ^I^Ir = f.degree()

....: ^I^In_lead = numerator.leading_coefficient()

....: ^I^If_lead = Rx(f).leading_coefficient()

....: ^I^Ia = d - (r-1)

....: ^I^Iif a >= 0:

....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))

....: ^I^I^IW += W_coeff*Rx(x^a)

....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()

....: ^I^I^Inumerator = Rx(numerator)

....: ^I^Iif a < 0:

....: ^I^I^Iprint('numerator', numerator)

....: ^I^I^IW += Rx(numerator/f.derivative())

....: ^I^I^Inumerator = Rx(0)

....: ^Iresult = result + superelliptic_function(C, y*W)

....: ^Ireturn result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint(A.diffn().regular_form())[?7h[?12l[?25h[?25l[?7lsage: int(A.diffn().regular_form())

[?7h[?12l[?25h[?2004lnumerator:  2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  0
0 dx
numerator:  3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126
((x^140 - 2*x^136 + x^132 + x^130 + x^126)/y) dx
numerator:  4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122
((x^140 + 2*x^136 + x^132 + x^130 - 2*x^128 - 2*x^124)/y) dx
numerator:  x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118
((x^140 + 2*x^136 - 2*x^132 + x^130 + x^128 + x^124 + 2*x^122 + 2*x^120 + x^118)/y) dx
numerator:  3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + 2*x^122 + 2*x^120 - x^118 - x^116 + x^114)/y) dx
numerator:  x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - x^116 + 2*x^114 - x^112 - x^110 + 2*x^108)/y) dx
numerator:  4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 - x^116 - x^112 - x^110 - x^106 + x^104)/y) dx
numerator:  2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + x^106)/y) dx
numerator:  3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 + 2*x^98 + x^96 + 2*x^94)/y) dx
numerator:  4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - 2*x^98 + x^96 - 2*x^94 - x^92 - x^90 + 2*x^88)/y) dx
numerator:  x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + x^96 - x^92 - x^90 - x^88 + x^86 - x^84)/y) dx
numerator:  x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 - x^92 - x^90 - x^86)/y) dx
numerator:  3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + 2*x^88 - x^86 + 2*x^84 - 2*x^82 - 2*x^80 - x^78)/y) dx
numerator:  2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 - x^86 + x^84 - 2*x^82 - 2*x^80 - 2*x^78 + 2*x^76 - 2*x^74)/y) dx
numerator:  x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 - 2*x^82 - 2*x^80 - 2*x^76)/y) dx
numerator:  4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - 2*x^80 + 2*x^78 - 2*x^76 + 2*x^74 - 2*x^72 - 2*x^70 - x^68)/y) dx
numerator:  4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + 2*x^78 - x^76 + 2*x^74 - x^68 + 2*x^66)/y) dx
numerator:  2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^68 - 2*x^66 - x^64)/y) dx
numerator:  2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + x^68 + x^66 - x^64 + x^62 + x^60 + x^56)/y) dx
numerator:  3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^62 + x^60 + x^58 - x^56 + 2*x^54)/y) dx
numerator:  4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^60 + 2*x^58 - x^56 - 2*x^54 - x^52 - x^50 + 2*x^48)/y) dx
numerator:  4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 + 2*x^58 - 2*x^54 + x^52 + x^50 + 2*x^48 + 2*x^46)/y) dx
numerator:  4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + x^52 + x^50 - x^48 - 2*x^46 - x^44)/y) dx
numerator:  3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 + x^52 + x^50 - 2*x^48 - 2*x^44)/y) dx
numerator:  4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 + x^50 - x^48 - x^44 - x^42 - x^40 + 2*x^38)/y) dx
numerator:  3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - x^48 + x^46 - x^44 + x^42 + x^40 + 2*x^38 + 2*x^36)/y) dx
numerator:  2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + x^46 - 2*x^44 + x^42 + x^40 + x^38 - x^36 - 2*x^34)/y) dx
numerator:  x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 + x^40 - 2*x^38)/y) dx
numerator:  3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - x^36 - 2*x^32 - 2*x^30 - 2*x^26)/y) dx
numerator:  x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 - 2*x^32 - 2*x^30 - 2*x^28 + 2*x^26 - 2*x^24)/y) dx
numerator:  3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 + 2*x^26 - 2*x^22 - 2*x^20 - x^18)/y) dx
numerator:  3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + 2*x^26 - x^24 - 2*x^22 - 2*x^20 - 2*x^18 + 2*x^16 - 2*x^14)/y) dx
numerator:  x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 - 2*x^22 - 2*x^20 + x^18 + x^16 + x^14)/y) dx
numerator:  4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 - 2*x^20 - 2*x^18 + x^16 - 2*x^14 - 2*x^12 - 2*x^10 - x^8)/y) dx
numerator:  3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 - 2*x^18 + 2*x^16 - 2*x^14 - x^8 + 2*x^6)/y) dx
numerator:  x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^16 + 2*x^14 - 2*x^8 - x^6 - 2*x^4)/y) dx
numerator:  2*x^10 + 2*x^6 + x^2 + 2
W:  x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 - x^8 + 2*x^6 - x^4)/y) dx
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [152], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())

Input In [151], in int(self)
     37 	if a < Integer(0):
     38 		print('numerator', numerator)
---> 39 		W += Rx(numerator/f.derivative())
     40 		numerator = Rx(Integer(0))
     41 result = result + superelliptic_function(C, y*W)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l1, A = decompositin_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1 = C1.x^126 + 2*C1.x^122 + 4*C1.x^118 + 2*C1.x^114 + 3*C1.x^108 + 2*C1.x^104 + C1.x^102 + 3*C1.x^92 + 3*C1.x^88 + 3*C1.x^84 + 4*C1.x^82 + C1.x^78 + C1.x^7
4

....:  + 3*C1.x^72 + C1.x^68 + 2*C1.x^66 + 3*C1.x^64 + C1.x^56 + 4*C1.x^54 + 3*C1.x^48 + 2*C1.x^46 + 3*C1.x^44 + C1.x^42 + 3*C1.x^38 + 2*C1.x^36 + C1.x^34 + 3*C1.
x

....: ^32 + 3*C1.x^26 + 2*C1.x^22 + C1.x^18 + C1.x^14 + 2*C1.x^12 + C1.x^8 + 2*C1.x^6 + C1.x^4 + 4*C1.x^2[?7h[?12l[?25h[?25l[?7lsage: A1 = C1.x^126 + 2*C1.x^122 + 4*C1.x^118 + 2*C1.x^114 + 3*C1.x^108 + 2*C1.x^104 + C1.x^102 + 3*C1.x^92 + 3*C1.x^88 + 3*C1.x^84 + 4*C1.x^82 + C1.x^78 + C1.x^7
4

....:  + 3*C1.x^72 + C1.x^68 + 2*C1.x^66 + 3*C1.x^64 + C1.x^56 + 4*C1.x^54 + 3*C1.x^48 + 2*C1.x^46 + 3*C1.x^44 + C1.x^42 + 3*C1.x^38 + 2*C1.x^36 + C1.x^34 + 3*C1.
x

....: ^32 + 3*C1.x^26 + 2*C1.x^22 + C1.x^18 + C1.x^14 + 2*C1.x^12 + C1.x^8 + 2*C1.x^6 + C1.x^4 + 4*C1.x^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1 = C1.x^126 + 2*C1.x^122 + 4*C1.x^118 + 2*C1.x^114 + 3*C1.x^108 + 2*C1.x^104 + C1.x^102 + 3*C1.x^92 + 3*C1.x^88 + 3*C1.x^84 + 4*C1.x^82 + C1.x^78 + C1.x^7
4

....:  + 3*C1.x^72 + C1.x^68 + 2*C1.x^66 + 3*C1.x^64 + C1.x^56 + 4*C1.x^54 + 3*C1.x^48 + 2*C1.x^46 + 3*C1.x^44 + C1.x^42 + 3*C1.x^38 + 2*C1.x^36 + C1.x^34 + 3*C1.
x

....: ^32 + 3*C1.x^26 + 2*C1.x^22 + C1.x^18 + C1.x^14 + 2*C1.x^12 + C1.x^8 + 2*C1.x^6 + C1.x^4 + 4*C1.x^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA

 

 [?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: A1 = A1 * C1.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lA1 = A1 * C1.y[?7h[?12l[?25h[?25l[?7l = Rx(A)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1).diffn()

[?7h[?12l[?25h[?2004l[?7h((x^10 + x^6 - 2*x^2 + 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1 = A1 * C1.y[?7h[?12l[?25h[?25l[?7l = Rx(A)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: A - A1

[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + x^32 + 2*x^30 + x^28 + 2*x^26 + 3*x^24 + 2*x^22 + x^20 + 2*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + 3*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.polynomial.derivative()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lpolynomial.derivative()[?7h[?12l[?25h[?25l[?7lsage: C1.polynomial.derivative()

[?7h[?12l[?25h[?2004l[?7h2*x^10 + x^6 + 2*x^2 + 4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA - A1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y/2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y/2).diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [158], in <cell line: 1>()
----> 1 (A - A1 - C.y/Integer(2)).diffn()

File <string>:75, in __truediv__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y/2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1C.y).difn()[?7h[?12l[?25h[?25l[?7l1.C.y).difn()[?7h[?12l[?25h[?25l[?7l2C.y).difn()[?7h[?12l[?25h[?25l[?7l*C.y).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l12*C.y).difn()[?7h[?12l[?25h[?25l[?7l/2*C.y).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - 1/2*C.y).diffn()

[?7h[?12l[?25h[?2004l[?7h((-2*x^10 + 2*x^6)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - 1/2*C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y).diffn()

[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y)

[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y)[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA(A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l2(A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l=(A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A2 = (A - A1 - C.y)/C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: A2

[?7h[?12l[?25h[?2004l[?7h(x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldnumerator()[?7h[?12l[?25h[?25l[?7lenumerator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lerator()[?7h[?12l[?25h[?25l[?7lerator()[?7h[?12l[?25h[?25l[?7loerator()[?7h[?12l[?25h[?25l[?7lmerator()[?7h[?12l[?25h[?25l[?7lierator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lator()[?7h[?12l[?25h[?25l[?7lnator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A2.function.numerator().quo_rem(A2.function.denominator())

[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4),
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2.function.numerator().quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A2.function.numerator()

[?7h[?12l[?25h[?2004l[?7hx^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l().quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A2.function.numerator().quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (A2.function.numerator()).quo_rem(A2.function.denominator())

[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4),
 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt.<t> = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF[?7h[?12l[?25h[?25l[?7lxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7ly, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C1.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l(A2.function.numeraor()).quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(A2.function.numerator()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7lx(A2.function.numerator()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7ly(A2.function.numerator()).quo_rem(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A2.function.denominator()[?7h[?12l[?25h[?25l[?7lA2.function.denominator()[?7h[?12l[?25h[?25l[?7lRA2.function.denominator()[?7h[?12l[?25h[?25l[?7lxA2.function.denominator()[?7h[?12l[?25h[?25l[?7lyA2.function.denominator()[?7h[?12l[?25h[?25l[?7l(A2.function.denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: Rxy(A2.function.numerator()).quo_rem(Rxy(A2.function.denominator()))

[?7h[?12l[?25h[?2004l[?7h(x^110 - x^106 + 2*x^100 + 2*x^96 + 2*x^92 - x^90 + 2*x^88 + 2*x^84 + x^82 + x^76 - 2*x^72 + x^70 - 2*x^68 - 2*x^66 - 2*x^64 - 2*x^62 - x^58 + x^56 - x^54 + x^52 + x^50 - x^48 + x^46 - x^44 - x^42 + 2*x^40 + 2*x^38 - 2*x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 - x^26 - 2*x^24 + 2*x^22 - 2*x^18 + x^16 - 2*x^14 - x^12 + 2*x^10 - 2*x^6 + 2,
 x^32 + 2*x^30 + 2*x^22 - x^20 + 2*x^18 - x^16 - 2*x^14 + 2*x^12 + x^10 - x^6 + x^4 - 2*x^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1 = om.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega1[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: omega1

[?7h[?12l[?25h[?2004l[?7h((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.polynomial.derivative()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.y.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^10 - 2*x^6 + x^2 + 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC1.y.difn()[?7h[?12l[?25h[?25l[?7lmC1.y.difn()[?7h[?12l[?25h[?25l[?7leC1.y.difn()[?7h[?12l[?25h[?25l[?7lgC1.y.difn()[?7h[?12l[?25h[?25l[?7laC1.y.difn()[?7h[?12l[?25h[?25l[?7l2C1.y.difn()[?7h[?12l[?25h[?25l[?7l =C1y.diffn()[?7h[?12l[?25h[?25l[?7l C1.y.difn()[?7h[?12l[?25h[?25l[?7loC1.y.difn()[?7h[?12l[?25h[?25l[?7lmC1.y.difn()[?7h[?12l[?25h[?25l[?7leC1.y.difn()[?7h[?12l[?25h[?25l[?7lgC1.y.difn()[?7h[?12l[?25h[?25l[?7laC1.y.difn()[?7h[?12l[?25h[?25l[?7l1C1.y.difn()[?7h[?12l[?25h[?25l[?7l C1.y.difn()[?7h[?12l[?25h[?25l[?7l-C1.y.difn()[?7h[?12l[?25h[?25l[?7l C1.y.difn()[?7h[?12l[?25h[?25l[?7l2C1.y.difn()[?7h[?12l[?25h[?25l[?7l*C1.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega2 = omega1 - 2*C1.y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2 = omega1 - 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: omega2

[?7h[?12l[?25h[?2004l[?7h((x^6 - x^2 - 2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega2.regular_form()

[?7h[?12l[?25h[?2004l[?7h((3*x^11 + 4*x^7 + 4*x^5 + 3*x^3 + x)*y) dx + (2*x^16 + 4*x^12 + x^10 + x^8 + x^6 + 3*x^4 + 3*x^2 + 4) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega2.int()

[?7h[?12l[?25h[?2004l[?7h((3*x^28 + 4*x^26 + 4*x^24 + x^22 + 4*x^20 + 4*x^16 + x^14 + 2*x^12 + 2*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 4)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.y.diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.y.diffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.is_smooth()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega2.int()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = omega1 - 2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lC1.y.diffn()[?7h[?12l[?25h[?25l[?7lomega1[?7h[?12l[?25h[?25l[?7lRxy(A2.function.numerator()).quo_rem(Rxy(A2.function.denominator()))[?7h[?12l[?25h[?25l[?7lF, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l(A2.function.numeraor()).quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7lA2.function.numerator()[?7h[?12l[?25h[?25l[?7l().quo_rem(A2.function.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7lsage: A2 = (A - A1 - C.y)/C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l - A1[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C.y).diffn()

[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = (A - A1 - C.y)/C.y[?7h[?12l[?25h[?25l[?7l - A1[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: A - A1 - C.y

[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy(A2.function.numerator()).quo_rem(Rxy(A2.function.denominator()))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: Rx

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4).factor()

[?7h[?12l[?25h[?2004l[?7h(x - 1)^3 * (x + 1)^3 * (x^5 - x + 2)^3 * (x^5 - x - 2)^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4).factor()[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lA - A1 - C.y[?7h[?12l[?25h[?25l[?7l(A - A1 - C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.y).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (A - A1 - C1.y).diffn()

[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA - A1 - C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA1 - C.y[?7h[?12l[?25h[?25l[?7lsage: A - A1 - C.y

[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.is_smooth()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 
3

....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54

....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 
4

....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 
+

....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y

....: print(A.diffn())

....: print(A.diffn().is_regular_on_U0())[?7h[?12l[?25h[?25l[?7lsage: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 
3

....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54

....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 
4

....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 
+

....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y

....: print(A.diffn())

....: print(A.diffn().is_regular_on_U0())

[?7h[?12l[?25h[?2004l((-2*x^6 + 2*x^2 - 1)/y) dx
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 
3

....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54
 

....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 
4

....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 
+

....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l.diffn().regular_form()

 

 

 

 [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion

 A.expansion         

 A.expansion_at_infty



 

 [?7h[?12l[?25h[?25l[?7l

 A.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 A.expansion         

 A.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-235 + 3*t^-195 + 2*t^-175 + 2*t^-155 + 3*t^-95 + 3*t^-55 + 3*t^-35 + 4*t + 2*t^9 + 4*t^13 + 4*t^25 + 4*t^29 + 2*t^33 + 4*t^37 + 2*t^41 + 3*t^49 + 2*t^65 + t^69 + 3*t^73 + 4*t^77 + 4*t^81 + t^85 + 4*t^93 + 4*t^97 + 2*t^105 + t^109 + 3*t^117 + 3*t^125 + 2*t^129 + t^137 + t^145 + 4*t^149 + 2*t^165 + 4*t^173 + 4*t^177 + 2*t^181 + 3*t^185 + t^197 + 2*t^201 + 3*t^205 + t^209 + 2*t^213 + 3*t^217 + 3*t^221 + 2*t^225 + 2*t^229 + 4*t^237 + t^245 + 4*t^249 + O(t^265)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7ldef int(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_pth_power(h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_pth_power(A)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [187], in <cell line: 1>()
----> 1 decomposition_g0_pth_power(A)

File <string>:5, in decomposition_g0_pth_power(fct)

File <string>:51, in int(self)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
   1329     normalize(x._numer, x._denom, self.p)
   1330     if nmod_poly_degree(x._denom) != 0:
-> 1331         raise ValueError("not integral")
   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:

ValueError: not integral
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1 = A1 * C1.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldiff().regular_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.diffn()

[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 
3

....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54

....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 
4

....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 
+

....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y

....: print(A.diffn())

....: print(A.diffn().is_regular_on_U0())

....: print(decomposition_g0_pth_power(A))[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()











A =((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 
3

*C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86+ 2*C1.x^84 + C1.x^82 +4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54


+ 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 
4

*C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36+ 2*C1.x^34+ 2*C1.x^32+ 2*C1.x^30+ 2*C1.x^28+ 4*C1.x^26+ C1.x^24+

 2*C1.x^22+ 3*C1.x^20+ 2*C1.x^18 + C1.x^14+ 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^44one))*C1.y

print(A.diffn())

.is_regular_on_U0())

 

 [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l









()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7lom1= ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 +4*C1.x^136 + 3*C1.x^134+ 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 
3

*C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54


+ 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 +4*C1.x^28 +3*C1.x^26 +2*C1.x^24 +3*C1.x^20 +2*C1.x^16 +C1.x^14 +4

*C1.x^12 +3*C1.x^10 +2*C1.x^8 + 3*C1.x^6 +2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^362x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 
+

 2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y

()

....: print(A.diffn().is_regular_on_U0())

....: print(decomposition_g0_pth_power(A))[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

(





)[?7h[?12l[?25h[?25l[?7l(





)



()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7limport itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 5

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....:     polynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I    print(polynom)[?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 5

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....:     polynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I    print(polynom)

[?7h[?12l[?25h[?2004l  Input In [190]
    polynom = superelliptic_function(C1, polynom)
    ^
TabError: inconsistent use of tabs and spaces in indentation

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 5

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....:     polynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 5

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....:     polynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)

[?7h[?12l[?25h[?2004l  Input In [191]
    polynom = superelliptic_function(C1, polynom)
    ^
TabError: inconsistent use of tabs and spaces in indentation

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 5

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....: ^Ipolynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7l....: ^I^Iprint(polynom)

....: [?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 5

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....: ^Ipolynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 7

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....: ^Ipolynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7l....: ^I^Iprint(polynom)

....: [?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 7

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....: ^Ipolynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)

....: 

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category()
    838 try:
--> 839     return self.__cached_methods[name]
    840 except KeyError:

KeyError: '_mpoly_base_ring'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:1114, in PolynomialRing_general._mpoly_base_ring(self, variables)
   1113 try:
-> 1114     return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
   1115 except AttributeError:

File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
    832 """
--> 833 return self.getattr_from_category(name)
    834 

File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
    847 
--> 848             attr = getattr_from_other_class(self, cls, name)
    849             self.__cached_methods[name] = attr

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
    355     dummy_error_message.name = name
--> 356     raise AttributeError(dummy_error_message)
    357 cdef PyObject* attr = instance_getattr(cls, name)

AttributeError: 'FpT_with_category' object has no attribute '_mpoly_base_ring'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Input In [193], in <cell line: 14>()
     15 polynom = sum(a[i] * x**i for i in range(N))
     16 polynom = superelliptic_function(C1, polynom)
---> 17 if polynom.diffn() == om1:
     18 	print(polynom)

File <string>:12, in __eq__(self, other)

File <string>:161, in reduce(self)

File <string>:263, in reduction(C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:921, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    919 
    920         elif isinstance(element, polynomial_element.Polynomial):
--> 921             if base_ring.has_coerce_map_from(element.parent()._mpoly_base_ring(self.variable_names())):
    922                 return self(element._mpoly_dict_recursive(self.variable_names(), base_ring))
    923 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:1114, in PolynomialRing_general._mpoly_base_ring(self, variables)
   1112 else:
   1113     try:
-> 1114         return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
   1115     except AttributeError:
   1116         return self.base_ring()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 7

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....: ^Ipolynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = C1.y*superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)[?7h[?12l[?25h[?25l[?7l....: ^I^Iprint(polynom)

....: [?7h[?12l[?25h[?25l[?7lsage: import itertools

....: p = 5

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: #f = (x^3 - x)^3 + x^3 - x

....: f = x^3 + x

....: f1 = f(x = x^5 - x)

....: C = superelliptic(f, m)

....: C1 = superelliptic(f1, m, prec = 500)

....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx

....: N = 7

....: lista = [GF(p) for _ in range(N)]

....: for a in itertools.product(*lista):

....: ^Ipolynom = sum(a[i] * x^i for i in range(N))

....: ^Ipolynom = C1.y*superelliptic_function(C1, polynom)

....: ^Iif polynom.diffn() == om1:

....: ^I^Iprint(polynom)

....: 

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [194], in <cell line: 14>()
     15 polynom = sum(a[i] * x**i for i in range(N))
     16 polynom = C1.y*superelliptic_function(C1, polynom)
---> 17 if polynom.diffn() == om1:
     18 	print(polynom)

File <string>:12, in __eq__(self, other)

File <string>:162, in reduce(self)

File <string>:7, in __init__(self, C, g)

File <string>:296, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1198 # Now coerce to a common parent and do the operation there
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:
   1202     self._record_exception()

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1313     x_elt = x
   1314 if y_map is not None:
-> 1315     y_elt = (<Map>y_map)._call_(y)
   1316 else:
   1317     y_elt = y

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:432, in sage.structure.coerce_maps.CallableConvertMap._call_()
    430         y = self._func(C, x)
    431     else:
--> 432         y = self._func(x)
    433 except Exception:
    434     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:324, in FractionField_generic._coerce_map_from_.<locals>.wrapper(x)
    323 def wrapper(x):
--> 324     return self._element_class(self, x.numerator(), x.denominator())

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1167, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
   1165     1/2/x
   1166 """
-> 1167 FractionFieldElement.__init__(self, parent, numerator, denominator,
   1168         coerce, reduce)
   1169 if not reduce:

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:121, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    119 if reduce and parent.is_exact():
    120     try:
--> 121         self.reduce()
    122     except ArithmeticError:
    123         pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
   1237 if self._is_reduced:
   1238     return
-> 1239 super(self.__class__, self).reduce()
   1240 self.normalize_leading_coefficients()
   1241 

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    162     return codomain.coerce(nnum/nden)
    163 
--> 164 cpdef reduce(self):
    165     """
    166     Reduce this fraction.

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    195     return
    196 try:
--> 197     g = self.__numerator.gcd(self.__denominator)
    198     if not g.is_unit():
    199         self.__numerator //= g

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4911         raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
   4912     else:
-> 4913         return doit(self, other)
   4914 
   4915 @coerce_binop

File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
    944 f1 = Num(f.numerator())
    945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4905 if tgt.ngens() > 1 and tgt._has_singular:
   4906     g = flatten(self).gcd(flatten(other))
-> 4907     return flatten.section()(g)
   4908 try:
   4909     doit = self._parent._base._gcd_univariate_polynomial

File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
    767 if P is D: # we certainly want to call _call_/with_args
    768     if not args and not kwds:
--> 769         return self._call_(x)
    770     return self._call_with_args(x, args, kwds)
    771 # Is there coercion?

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:362, in UnflatteningMorphism._call_(self, p)
    359     Morphism.__init__(self, hom)
    360     self._repr_type_str = 'Unflattening'
--> 362 def _call_(self, p):
    363     """
    364     Evaluate an unflattening morphism.
    365 
   (...)
    377         ....:        assert z == g(f(z))
    378     """
    379     index = [0]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h((-2*x^6 + 2*x^2 - 1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.cartier().cartier().inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7linv_catier().inv_cartier()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint().diffn[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.int()

[?7h[?12l[?25h[?2004l[?7h((4*x^28 + 2*x^26 + 2*x^24 + 3*x^22 + 2*x^20 + 2*x^16 + 3*x^14 + x^12 + x^10 + 2*x^8 + 4*x^6 + 2*x^4 + x^2 + 2)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: om1.curve

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.genus()

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [GF(p) for _ in range(N)][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [200], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:11, in <module>

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:26, in de_rham_witt_lift(cech_class, prec)

File <string>:90, in diffn(self, dy_w)

File <string>:99, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:94, in diffn(self)

File /ext/sage/9.7/src/sage/categories/quotient_fields.py:610, in QuotientFields.ElementMethods.derivative(self, *args)
    580 r"""
    581 The derivative of this rational function, with respect to variables
    582 supplied in args.
   (...)
    607     2/(x^3 + 3*x^2*y + 3*x*y^2 + y^3)
    608 """
    609 from sage.misc.derivative import multi_derivative
--> 610 return multi_derivative(self, args)

File /ext/sage/9.7/src/sage/misc/derivative.pyx:222, in sage.misc.derivative.multi_derivative()
    220 
    221     for arg in derivative_parse(args):
--> 222         F = F._derivative(arg)
    223     return F
    224 

File /ext/sage/9.7/src/sage/categories/quotient_fields.py:671, in QuotientFields.ElementMethods._derivative(self, var)
    613 r"""
    614 Returns the derivative of this rational function with respect to the
    615 variable ``var``.
   (...)
    668     (-t + 1)/(t^3 + 3*t^2 + 3*t + 1)
    669 """
    670 R = self.parent()
--> 671 if var in R.gens():
    672     var = R.ring()(var)
    674 num = self.numerator()

File /ext/sage/9.7/src/sage/structure/element.pyx:1112, in sage.structure.element.Element.__richcmp__()
   1110         return (<Element>self)._richcmp_(other, op)
   1111     else:
-> 1112         return coercion_model.richcmp(self, other, op)
   1113 
   1114 cpdef _richcmp_(left, right, int op):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
   1971 # Coerce to a common parent
   1972 try:
-> 1973     x, y = self.canonical_coercion(x, y)
   1974 except (TypeError, NotImplementedError):
   1975     pass

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1313     x_elt = x
   1314 if y_map is not None:
-> 1315     y_elt = (<Map>y_map)._call_(y)
   1316 else:
   1317     y_elt = y

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^18 + 4*x^16 + 4*x^14 + x^8 + x^6 + x^4)/(x^4 + 2*x^2 + 1))*y]), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y), [(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^2 + 1)/(x^4 + 2*x^2 + 1))*y])),
 ([(1/(x^2 + 1))*y] d[x] + V(((-2*x^7 - 2*x^5 - 2*x^3 + x)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^23 + 4*x^21 + 4*x^19 + x^13 + x^11 + x^9)/(x^4 + 2*x^2 + 1))*y]), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y), [(1/(x^4 + x^2))*y] d[x] + V(((-2*x^6 + x^4 - 2*x^2 - 2)/(x^7*y + 2*x^5*y + x^3*y)) dx) + dV([(3*x/(x^4 + 2*x^2 + 1))*y]))]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laom.verschiebung() == aom0.verschiebung() + mult_by_p(h.diffn())[?7h[?12l[?25h[?25l[?7lux = OM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7ltom(B1[0]).coordinaes(basis = B1)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[4]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [203], in <cell line: 1>()
----> 1 autom(B[Integer(0)]).coordinates(basis=B)

File <string>:109, in coordinates(self, basis, prec, info)

File <string>:59, in coordinates(self)

File <string>:93, in coordinates(self, basis)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
   1249     return num
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC1.genus()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [206], in <cell line: 1>()
----> 1 autom(B[Integer(0)]).coordinates(basis=B)

File <string>:117, in coordinates(self, basis, prec, info)

File <string>:88, in div_by_p(self, info)

TypeError: cannot unpack non-iterable superelliptic_function object
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[0]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B)

[?7h[?12l[?25h[?2004l[?7h[4, 6]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [209], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:13, in <module>

File <string>:91, in regular_drw_cech(cocycle)

File <string>:83, in regular_drw_form(omega)

AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....:     C = omega.curve

....:     omega_aux = omega.r()

....:     omega_aux = omega_aux.regular_form()

....:     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....:     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....:     aux.h2 += fct^p

....:     aux.h2, A = decomposition_g0_pth_power(aux.h2)

....:     aux.omega += (A.diffn()).inv_cartier()

....:     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....:     return result[?7h[?12l[?25h[?25l[?7l....:     return result

....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....:     C = omega.curve

....:     omega_aux = omega.r()

....:     omega_aux = omega_aux.regular_form()

....:     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....:     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....:     aux.h2 += fct^p

....:     aux.h2, A = decomposition_g0_pth_power(aux.h2)

....:     aux.omega += (A.diffn()).inv_cartier()

....:     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....:     return result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(OM)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr_drw_form(OM)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(B[0].omega0)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
   1249 

TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [211], in <cell line: 1>()
----> 1 regular_drw_form(B[Integer(0)].omega0)

Input In [210], in regular_drw_form(omega)
      3 omega_aux = omega.r()
      4 omega_aux = omega_aux.regular_form()
----> 5 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
      6 aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
      7 aux.h2 += fct**p

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

    [... skipping similar frames: __rmul__ at line 43 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times), sage.structure.element.Element.__mul__ at line 1528 (2 times)]

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[0].regular_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].regular_form()[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....:     C = omega.curve

....:     p = C.characteristic

....:     omega_aux = omega.r()

....:     omega_aux = omega_aux.regular_form()

....:     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....:     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....:     aux.h2 += fct^p

....:     aux.h2, A = decomposition_g0_pth_power(aux.h2)

....:     aux.omega += (A.diffn()).inv_cartier()

....:     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....:     return result[?7h[?12l[?25h[?25l[?7l....:     return result

....: [?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....:     C = omega.curve

....:     p = C.characteristic

....:     omega_aux = omega.r()

....:     omega_aux = omega_aux.regular_form()

....:     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....:     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....:     aux.h2 += fct^p

....:     aux.h2, A = decomposition_g0_pth_power(aux.h2)

....:     aux.omega += (A.diffn()).inv_cartier()

....:     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....:     return result

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_form(omega):

....:     C = omega.curve

....:     p = C.characteristic

....:     omega_aux = omega.r()

....:     omega_aux = omega_aux.regular_form()

....:     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

....:     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)

....:     aux.h2 += fct^p

....:     aux.h2, A = decomposition_g0_pth_power(aux.h2)

....:     aux.omega += (A.diffn()).inv_cartier()

....:     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)

....:     return result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(B[0].omega0)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7llar_drw_form(B[0].omega0)[?7h[?12l[?25h[?25l[?7lsage: regular_drw_form(B[0].omega0)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
   1249 

TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [215], in <cell line: 1>()
----> 1 regular_drw_form(B[Integer(0)].omega0)

Input In [214], in regular_drw_form(omega)
      4 omega_aux = omega.r()
      5 omega_aux = omega_aux.regular_form()
----> 6 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
      7 aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
      8 aux.h2 += fct**p

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
   2412         return x
   2413 
-> 2414     return coercion_model.bin_op(left, right, operator.mul)
   2415 
   2416 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

    [... skipping similar frames: __rmul__ at line 43 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times), sage.structure.element.Element.__mul__ at line 1528 (2 times)]

File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
   1526     if not err:
   1527         return (<Element>right)._mul_long(value)
-> 1528     return coercion_model.bin_op(left, right, mul)
   1529 except TypeError:
   1530     return NotImplemented

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx.diffn().expnson_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx.diffn().expnson_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l[?7h[1] d[x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOB[0].omega0[?7h[?12l[?25h[?25l[?7lMB[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l=B[0].omega0[?7h[?12l[?25h[?25l[?7l B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7lo = B[0].omega0[?7h[?12l[?25h[?25l[?7lm = B[0].omega0[?7h[?12l[?25h[?25l[?7le = B[0].omega0[?7h[?12l[?25h[?25l[?7lg = B[0].omega0[?7h[?12l[?25h[?25l[?7la = B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: omega = B[0].omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega.r()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega.r()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega_aux.regular_form()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega_aux.regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [220], in <cell line: 1>()
----> 1 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

File <string>:65, in __mul__(self, other)

File <string>:64, in __mul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l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omega_aux.dx.teichmuller()*C.x.teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [221], in <cell line: 1>()
----> 1 omega_aux.dx.teichmuller()*C.x.teichmuller().diffn()

File <string>:65, in __mul__(self, other)

File <string>:64, in __mul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7laux.dx.teichmuller()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega_aux.dx.teichmuller()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7laomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7lromega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7leomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7lnomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7ltomega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7l(omega_aux.dx.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.dx.teichmuller())

[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_witt'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.dx.teichmuller().t.function)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega

[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = omga_ax.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lomega_aux.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = omga_ax.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lomega_aux.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller().t.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.xteichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [226], in <cell line: 1>()
----> 1 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()

File <string>:65, in __mul__(self, other)

File <string>:64, in __mul__(self, other)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller().t.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.xteichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega_aux =omega_ux.regular_form()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega_aux.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [227], in <cell line: 1>()
----> 1 omega_aux = omega_aux.regular_form()

AttributeError: 'superelliptic_regular_form' object has no attribute 'regular_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega_aux.regular_form()[?7h[?12l[?25h[?25l[?7laux = omega- omeg_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lparent(omega_aux.dx.teichmuller().t.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lomega_aux.dx.teichmuller()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.xteichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lomega_aux =omega_ux.regular_form()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l_aux = omega.r()[?7h[?12l[?25h[?25l[?7lsage: omega_aux = omega.r()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpamega_aux.function[?7h[?12l[?25h[?25l[?7lamega_aux.function[?7h[?12l[?25h[?25l[?7lramega_aux.function[?7h[?12l[?25h[?25l[?7leamega_aux.function[?7h[?12l[?25h[?25l[?7lnamega_aux.function[?7h[?12l[?25h[?25l[?7ltamega_aux.function[?7h[?12l[?25h[?25l[?7l(amega_aux.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmega_aux.function[?7h[?12l[?25h[?25l[?7lomega_aux.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.function)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [229], in <cell line: 1>()
----> 1 parent(omega_aux.function)

AttributeError: 'superelliptic_form' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(omega_aux.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lfor)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(omega_aux.form)

[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega_aux = omega.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: omega.curve

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.xpansion_at_inty[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, (1/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.diffn()[?7h[?12l[?25h[?25l[?7lsage: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 
3

....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54
 

....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 + 3*C1.x^20 + 2*C1.x^16 + C1.x^14 + 
4

....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30 + 2*C1.x^28 + 4*C1.x^26 + C1.x^24 
+

....:  2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC

 

 

 

 [?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = C.de_rham_basis[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [234], in <cell line: 1>()
----> 1 A = C.de_rham_basis[Integer(0)]

TypeError: 'method' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.de_rham_basis[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0][?7h[?12l[?25h[?25l[?7l)[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = C.de_rham_basis()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: A = A.omega0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = A.omega0[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpA.form[?7h[?12l[?25h[?25l[?7laA.form[?7h[?12l[?25h[?25l[?7lrA.form[?7h[?12l[?25h[?25l[?7leA.form[?7h[?12l[?25h[?25l[?7lnA.form[?7h[?12l[?25h[?25l[?7ltA.form[?7h[?12l[?25h[?25l[?7l(A.form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(A.form)

[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0].omega0[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7laB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7lrB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7leB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7lnB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7ltB[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7l(B[0].omega0.omega.form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(B[0].omega0.omega.form)

[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef regular_drw_form(omega):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift

 de_rham_witt_lift      

 de_rham_witt_lift_form0

 de_rham_witt_lift_form8



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 de_rham_witt_lift      





 <unknown> [?7h[?12l[?25h[?25l[?7l_form0

 de_rham_witt_lift      

 de_rham_witt_lift_form0[?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift_form0(C.dx)

[?7h[?12l[?25h[?2004l[?7h[1] d[x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAde_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = de_rham_witt_lift_form0(C.dx)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lA = de_rham_witt_lift_form0(C.dx)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpA.omega.form)[?7h[?12l[?25h[?25l[?7laA.omega.form)[?7h[?12l[?25h[?25l[?7lrA.omega.form)[?7h[?12l[?25h[?25l[?7leA.omega.form)[?7h[?12l[?25h[?25l[?7lnA.omega.form)[?7h[?12l[?25h[?25l[?7ltA.omega.form)[?7h[?12l[?25h[?25l[?7l(A.omega.form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(A.omega.form)

[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A.omega.form)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7l.form)[?7h[?12l[?25h[?25l[?7lh.form)[?7h[?12l[?25h[?25l[?7l1.form)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lfor)[?7h[?12l[?25h[?25l[?7lfo)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(A.h1.function)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.function)[?7h[?12l[?25h[?25l[?7l2.function)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: parent(A.h2.function)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12, in <module>

NameError: name 'C1' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((2*x^215 + 2*x^211 + 2*x^207 + 3*x^205 + 2*x^203 + 4*x^201 + 3*x^197 + 4*x^189 + 3*x^185 + x^181 + 4*x^179 + 4*x^177 + 2*x^175 + 2*x^173 + 4*x^171 + 2*x^169 + x^167 + 4*x^165 + 2*x^163 + 3*x^161 + x^159 + x^155 + 2*x^151 + 4*x^149 + 3*x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 3*x^137 + 4*x^135 + 4*x^133 + 2*x^131 + 4*x^129 + x^127 + x^125 + 4*x^123 + 2*x^121 + x^117 + 4*x^115 + x^113 + 2*x^111 + x^109 + 2*x^105 + x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 4*x^93 + 4*x^91 + 2*x^89 + x^87 + x^85 + x^83 + x^81 + x^79 + 3*x^77 + 4*x^75 + 4*x^71 + 3*x^69 + x^67 + 2*x^63 + 3*x^61 + x^59 + x^57 + x^55 + 3*x^51 + 3*x^47 + x^43 + x^41 + 4*x^37 + 4*x^33 + 4*x^31 + 4*x^29 + 4*x^25 + 2*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^220 + 4*x^210 + 3*x^206 + 2*x^204 + 2*x^202 + 3*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^190 + 4*x^180 + x^176 + 2*x^174 + 2*x^170 + 3*x^168 + 4*x^166 + 2*x^164 + 2*x^162 + x^158 + 2*x^156 + 3*x^154 + 2*x^152 + 3*x^150 + 3*x^148 + 2*x^146 + 2*x^142 + 2*x^140 + x^134 + 2*x^132 + 3*x^130 + 2*x^128 + x^126 + 3*x^124 + 4*x^122 + x^120 + 2*x^118 + 4*x^116 + 2*x^114 + 3*x^108 + 4*x^104 + 2*x^100 + 3*x^98 + 3*x^94 + 3*x^92 + 4*x^90 + 4*x^88 + 2*x^86 + x^84 + x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + x^62 + 4*x^60 + 2*x^58 + 2*x^54 + 3*x^52 + 3*x^50 + 4*x^44 + x^42 + 3*x^40 + 2*x^32 + x^26 + 2*x^24 + 2*x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12, in <module>

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:25, in de_rham_witt_lift(cech_class, prec)

File <string>:15, in de_rham_witt_lift_form8(omega)

File <string>:90, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:149, in auxilliary_derivative(P)

    [... skipping similar frames: auxilliary_derivative at line 149 (1 times)]

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

    [... skipping similar frames: __rmul__ at line 55 (2 times), sage.rings.integer.Integer.__mul__ at line 1964 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times)]

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:53, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:44, in __rmul__(self, constant)

File <string>:7, in __init__(self, C, g)

File <string>:296, in reduction_form(C, g)

File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
   1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
-> 1516     return coercion_model.bin_op(left, right, mul)
   1517 
   1518 cdef long value

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
   1512 cdef int cl = classify_elements(left, right)
   1513 if HAVE_SAME_PARENT(cl):
-> 1514     return (<Element>left)._mul_(right)
   1515 if BOTH_ARE_ELEMENT(cl):
   1516     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:669, in sage.rings.fraction_field_element.FractionFieldElement._mul_()
    667 try:
    668     d1 = rnum.gcd(sden)
--> 669     d2 = snum.gcd(rden)
    670     if not d1.is_unit():
    671         rnum = rnum // d1

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4911         raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
   4912     else:
-> 4913         return doit(self, other)
   4914 
   4915 @coerce_binop

File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
    944 f1 = Num(f.numerator())
    945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()

File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
   4492 def new_method(self, other, *args, **kwargs):
   4493     if have_same_parent(self, other):
-> 4494         return method(self, other, *args, **kwargs)
   4495     else:
   4496         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
   4905 if tgt.ngens() > 1 and tgt._has_singular:
   4906     g = flatten(self).gcd(flatten(other))
-> 4907     return flatten.section()(g)
   4908 try:
   4909     doit = self._parent._base._gcd_univariate_polynomial

File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
    767 if P is D: # we certainly want to call _call_/with_args
    768     if not args and not kwds:
--> 769         return self._call_(x)
    770     return self._call_with_args(x, args, kwds)
    771 # Is there coercion?

File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
    786     return self._call_with_args(x, args, kwds)
    787 
--> 788 cpdef Element _call_(self, x):
    789     """
    790     Call method with a single argument, not implemented in the base class.

File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:380, in UnflatteningMorphism._call_(self, p)
    363 """
    364 Evaluate an unflattening morphism.
    365 
   (...)
    377     ....:        assert z == g(f(z))
    378 """
    379 index = [0]
--> 380 for R, _ in reversed(self._intermediate_rings):
    381     index.append(index[-1] + len(R.gens()))
    382 newpol = [{} for _ in self._intermediate_rings]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((x^37 + 2*x^35 + x^33 + 4*x^29 + 4*x^27 + x^25 + x^23 + 2*x^19 + 4*x^17 + 2*x^15 + 4*x^9 + x^7 + 3*x^3)*y) dx + (x^38 + x^36 + 4*x^34 + 4*x^32 + 4*x^30 + 2*x^26 + 4*x^22 + 2*x^20 + 2*x^18 + 3*x^16 + 3*x^14 + 4*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((x^42 + 2*x^40 + x^38 + 4*x^34 + 4*x^32 + x^30 + x^28 + 2*x^24 + 3*x^22 + 4*x^18)*y) dx + (x^43 + x^41 + 4*x^39 + 4*x^37 + 4*x^35 + 2*x^31 + 4*x^27 + 2*x^25 + x^23 + 2*x^21 + 4*x^19 + x^17) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((2*x^215 + 2*x^211 + 2*x^207 + 3*x^205 + 2*x^203 + 4*x^201 + 3*x^197 + 4*x^189 + 3*x^185 + x^181 + 4*x^179 + 4*x^177 + 2*x^175 + 2*x^173 + 4*x^171 + 2*x^169 + x^167 + 4*x^165 + 2*x^163 + 3*x^161 + x^159 + x^155 + 2*x^151 + 4*x^149 + 3*x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 3*x^137 + 4*x^135 + 4*x^133 + 2*x^131 + 4*x^129 + x^127 + x^125 + 4*x^123 + 2*x^121 + x^117 + 4*x^115 + x^113 + 2*x^111 + x^109 + 2*x^105 + x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 4*x^93 + 4*x^91 + 2*x^89 + x^87 + x^85 + x^83 + x^81 + x^79 + 3*x^77 + 4*x^75 + 4*x^71 + 3*x^69 + x^67 + 2*x^63 + 3*x^61 + x^59 + x^57 + x^55 + 3*x^51 + 3*x^47 + x^43 + x^41 + 4*x^37 + 4*x^33 + 4*x^31 + 4*x^29 + 4*x^25 + 2*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^220 + 4*x^210 + 3*x^206 + 2*x^204 + 2*x^202 + 3*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^190 + 4*x^180 + x^176 + 2*x^174 + 2*x^170 + 3*x^168 + 4*x^166 + 2*x^164 + 2*x^162 + x^158 + 2*x^156 + 3*x^154 + 2*x^152 + 3*x^150 + 3*x^148 + 2*x^146 + 2*x^142 + 2*x^140 + x^134 + 2*x^132 + 3*x^130 + 2*x^128 + x^126 + 3*x^124 + 4*x^122 + x^120 + 2*x^118 + 4*x^116 + 2*x^114 + 3*x^108 + 4*x^104 + 2*x^100 + 3*x^98 + 3*x^94 + 3*x^92 + 4*x^90 + 4*x^88 + 2*x^86 + x^84 + x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + x^62 + 4*x^60 + 2*x^58 + 2*x^54 + 3*x^52 + 3*x^50 + 4*x^44 + x^42 + 3*x^40 + 2*x^32 + x^26 + 2*x^24 + 2*x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) )
( [(3*x^6 + 2*x^2)*y] d[x] + [2*x^11 + x^7 + 2*x^3 + 3*x] d[y] + V(((2*x^220 + 2*x^216 + 2*x^212 + 4*x^210 + 2*x^208 + 4*x^202 + 4*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^192 + 3*x^190 + x^186 + x^184 + 4*x^182 + 2*x^180 + 2*x^178 + 3*x^176 + 4*x^174 + 4*x^172 + 2*x^170 + 4*x^168 + 2*x^164 + x^160 + 4*x^158 + 3*x^156 + 4*x^154 + x^152 + 2*x^150 + 4*x^148 + x^138 + x^136 + 3*x^134 + 3*x^128 + 3*x^126 + 4*x^124 + 3*x^122 + x^120 + 3*x^118 + 3*x^116 + 3*x^114 + 2*x^110 + 3*x^108 + 4*x^106 + 4*x^104 + 2*x^102 + 4*x^98 + 2*x^94 + 4*x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + x^76 + 4*x^74 + 2*x^72 + x^70 + 3*x^68 + 3*x^66 + 2*x^64 + 3*x^58 + x^56 + 2*x^50 + x^48 + 2*x^46 + x^44 + 4*x^42 + 2*x^40 + x^38 + 4*x^36 + x^32 + 4*x^30 + 2*x^28 + x^26 + 4*x^24 + 3*x^22 + 4*x^18 + 3*x^16 + x^14 + 3*x^12 + 2*x^8)*y) dx + (3*x^225 + 3*x^215 + 3*x^211 + 2*x^209 + 2*x^207 + x^203 + x^201 + x^197 + 3*x^195 + 3*x^193 + x^191 + 2*x^189 + x^181 + 2*x^179 + 3*x^175 + 3*x^173 + x^171 + 4*x^169 + 3*x^167 + 3*x^163 + 2*x^161 + 4*x^159 + x^157 + 2*x^155 + x^149 + 4*x^147 + 4*x^145 + 2*x^143 + 3*x^141 + x^139 + x^135 + 2*x^133 + x^131 + 2*x^129 + 4*x^127 + x^125 + 2*x^123 + 4*x^121 + x^119 + 2*x^117 + 3*x^115 + 4*x^113 + 3*x^111 + 4*x^109 + 2*x^107 + x^105 + x^103 + x^101 + 4*x^99 + 3*x^97 + 2*x^91 + 4*x^89 + 4*x^87 + 3*x^85 + 3*x^83 + 3*x^81 + 3*x^77 + x^75 + x^73 + 2*x^71 + 2*x^69 + 4*x^67 + 4*x^65 + x^63 + 4*x^61 + 4*x^59 + x^57 + 4*x^55 + 2*x^53 + 2*x^51 + 3*x^49 + 4*x^45 + x^43 + 4*x^37 + 2*x^35 + x^33 + 3*x^31 + 4*x^27 + 2*x^23 + 4*x^21 + 3*x^15 + 2*x^9 + 3*x^7) dy) + dV(0), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y) )
( [(3*x^7 + 2*x^3)*y] d[x] + [2*x^12 + x^8 + 2*x^4 + 3*x^2] d[y] + V(((2*x^225 + 2*x^221 + 2*x^217 + 2*x^213 + x^211 + 3*x^205 + 2*x^203 + 4*x^201 + 4*x^199 + 3*x^197 + 3*x^195 + x^191 + 3*x^189 + 4*x^187 + 2*x^185 + 2*x^183 + 2*x^181 + x^179 + 2*x^177 + x^173 + 2*x^171 + 3*x^169 + x^165 + 3*x^163 + 4*x^161 + 4*x^159 + 4*x^157 + 3*x^151 + 2*x^147 + x^145 + 3*x^143 + 2*x^139 + 4*x^137 + 4*x^135 + 2*x^133 + 4*x^131 + 3*x^129 + 4*x^125 + x^117 + x^115 + x^113 + x^109 + 2*x^105 + 4*x^103 + 4*x^99 + 3*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 4*x^87 + 2*x^85 + 2*x^83 + x^81 + 4*x^79 + 2*x^77 + 4*x^75 + x^73 + x^71 + 4*x^69 + x^67 + 2*x^65 + 4*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + x^49 + 4*x^47 + x^45 + x^43 + 3*x^41 + 4*x^39 + x^37 + 4*x^35 + 3*x^33 + x^31 + 2*x^29 + x^27 + 2*x^25 + 2*x^23 + 4*x^21 + 4*x^19 + x^13 + 4*x^11 + 3*x^9 + 4*x^7 + x^3)*y) dx + (3*x^230 + 2*x^220 + 3*x^216 + 2*x^214 + 2*x^212 + 2*x^210 + x^208 + x^204 + 2*x^202 + 2*x^200 + x^198 + 2*x^196 + 4*x^194 + x^190 + x^186 + 2*x^184 + 4*x^180 + 3*x^178 + 3*x^176 + x^174 + 4*x^172 + 2*x^166 + x^160 + 2*x^158 + 3*x^156 + 2*x^154 + x^152 + x^150 + 4*x^148 + x^146 + x^144 + 3*x^142 + 4*x^140 + 2*x^138 + x^136 + x^134 + 4*x^132 + 2*x^128 + 4*x^126 + 4*x^122 + 3*x^120 + 2*x^108 + 3*x^106 + 2*x^104 + 3*x^102 + x^100 + x^98 + 3*x^96 + x^94 + x^92 + 4*x^90 + x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + x^74 + 4*x^72 + x^68 + 2*x^66 + x^64 + 2*x^60 + 4*x^58 + 2*x^56 + 2*x^54 + 2*x^48 + 3*x^46 + 2*x^44 + x^42 + x^40 + 3*x^38 + 2*x^36 + 3*x^30 + 2*x^28 + 2*x^26 + 3*x^24 + 4*x^22 + x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + 4*x^10 + x^4 + 4*x^2) dy) + dV(0), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y) )
( [(3*x^8 + 2*x^4)*y] d[x] + [2*x^13 + x^9 + 2*x^5 + 3*x^3] d[y] + V(((2*x^230 + 2*x^226 + 2*x^222 + x^220 + 2*x^218 + 2*x^216 + x^212 + 2*x^210 + 3*x^208 + x^206 + 4*x^204 + 2*x^202 + 3*x^200 + x^196 + 4*x^192 + 2*x^190 + 2*x^188 + x^186 + 3*x^184 + 3*x^180 + 3*x^178 + 4*x^176 + 4*x^174 + x^170 + 2*x^168 + 4*x^164 + 2*x^162 + 3*x^160 + x^158 + x^156 + 4*x^152 + 2*x^150 + 4*x^146 + x^144 + 3*x^142 + 3*x^140 + x^138 + 2*x^134 + 2*x^132 + 3*x^130 + 2*x^128 + 3*x^126 + 2*x^124 + 3*x^122 + x^120 + 3*x^114 + 4*x^112 + 4*x^110 + x^108 + x^106 + 3*x^104 + x^102 + 4*x^100 + 4*x^98 + x^96 + 4*x^94 + 3*x^92 + 4*x^88 + 4*x^86 + 3*x^84 + 3*x^82 + 4*x^80 + 3*x^78 + x^76 + 4*x^74 + 2*x^72 + 3*x^70 + 2*x^68 + x^66 + 2*x^64 + 4*x^62 + 2*x^54 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + 4*x^44 + 3*x^40 + 3*x^38 + 4*x^36 + 4*x^34 + 3*x^30 + 3*x^28 + 4*x^24 + 4*x^22 + x^16 + 2*x^14 + x^12 + 4*x^8)*y) dx + (3*x^235 + x^225 + 3*x^221 + 2*x^219 + 2*x^217 + 4*x^215 + x^213 + 4*x^211 + 2*x^209 + 3*x^207 + x^205 + 4*x^203 + 3*x^201 + x^199 + 2*x^195 + x^191 + 2*x^189 + 3*x^183 + 3*x^179 + 2*x^173 + 2*x^171 + x^169 + 4*x^167 + 4*x^163 + x^161 + 3*x^159 + 3*x^157 + 3*x^155 + x^153 + 4*x^151 + x^149 + x^147 + 2*x^145 + 2*x^143 + x^141 + 4*x^137 + 3*x^135 + 2*x^133 + 4*x^131 + 4*x^129 + x^127 + 3*x^125 + x^123 + x^121 + 2*x^119 + 4*x^117 + x^113 + 4*x^111 + 4*x^109 + 4*x^105 + 3*x^103 + 4*x^101 + 4*x^99 + 2*x^95 + x^89 + 3*x^87 + 4*x^85 + x^83 + 2*x^81 + 3*x^79 + x^77 + 4*x^75 + x^71 + 4*x^69 + 3*x^67 + 4*x^65 + 2*x^63 + 3*x^61 + 3*x^59 + 3*x^57 + x^55 + 4*x^53 + 2*x^51 + 2*x^49 + 3*x^47 + x^45 + 3*x^43 + 3*x^41 + 4*x^39 + 3*x^37 + 4*x^35 + 4*x^33 + 3*x^27 + 3*x^25 + 4*x^23 + 3*x^21 + 2*x^19 + 3*x^17 + x^15 + 4*x^9 + x^7) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y) )
( [(3*x^9 + 2*x^5)*y] d[x] + [2*x^14 + x^10 + 2*x^6 + 3*x^4] d[y] + V(((2*x^235 + 2*x^231 + 2*x^227 + 2*x^225 + 2*x^223 + 3*x^221 + 2*x^217 + x^215 + 4*x^213 + 3*x^211 + 4*x^209 + x^207 + 3*x^205 + x^201 + 2*x^199 + 4*x^197 + 2*x^195 + 2*x^193 + 3*x^187 + x^185 + x^181 + x^175 + x^173 + x^171 + 4*x^169 + x^165 + 2*x^163 + 4*x^161 + x^157 + 3*x^155 + 2*x^153 + 3*x^151 + 2*x^147 + 2*x^145 + x^141 + x^139 + 4*x^137 + 2*x^135 + 4*x^133 + x^131 + 4*x^129 + 4*x^123 + 4*x^121 + 2*x^117 + x^115 + 2*x^113 + 4*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 4*x^101 + x^99 + 2*x^95 + 3*x^93 + 3*x^91 + 3*x^89 + 3*x^85 + 4*x^83 + 2*x^77 + 4*x^75 + x^73 + x^69 + x^65 + 2*x^61 + 3*x^59 + 2*x^57 + 4*x^55 + x^53 + x^51 + 4*x^49 + 2*x^47 + x^45 + 4*x^43 + 3*x^41 + 2*x^37 + x^35 + x^33 + x^31 + 4*x^29 + 3*x^27 + x^25 + 3*x^23 + 3*x^19 + 3*x^17 + 2*x^11 + 4*x^9 + 2*x^7 + 3*x^3)*y) dx + (3*x^240 + 3*x^226 + 2*x^224 + 2*x^222 + x^220 + x^218 + 3*x^216 + 3*x^214 + 4*x^212 + 2*x^208 + 4*x^206 + 3*x^204 + 3*x^200 + x^196 + 2*x^194 + x^190 + 3*x^188 + 2*x^186 + x^182 + 4*x^178 + 2*x^176 + 2*x^174 + 3*x^172 + 4*x^170 + x^168 + 4*x^166 + 4*x^164 + 3*x^158 + 2*x^156 + x^154 + 4*x^152 + 2*x^148 + x^146 + 4*x^144 + 4*x^142 + x^140 + 2*x^138 + 4*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 2*x^128 + 2*x^126 + 4*x^124 + 3*x^122 + 4*x^120 + x^116 + x^112 + 4*x^110 + 2*x^108 + 4*x^104 + 3*x^102 + 3*x^100 + x^98 + 2*x^96 + x^92 + 2*x^90 + 2*x^88 + 3*x^86 + 3*x^84 + 3*x^82 + 3*x^80 + x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 2*x^66 + 3*x^64 + 3*x^62 + x^60 + 4*x^58 + 2*x^56 + 3*x^54 + 3*x^50 + 4*x^46 + 4*x^42 + x^40 + 3*x^38 + 4*x^34 + x^30 + 3*x^28 + 2*x^24 + 4*x^22 + x^20 + 3*x^18 + x^16 + 4*x^14 + x^12 + 2*x^10 + 3*x^4 + 2*x^2) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y) )
( [(3*x^10 + 2*x^6)*y] d[x] + [2*x^15 + x^11 + 2*x^7 + 3*x^5] d[y] + V(((2*x^240 + 2*x^236 + 2*x^232 + 3*x^230 + 2*x^228 + 4*x^226 + 3*x^222 + 4*x^214 + 3*x^210 + x^206 + 4*x^204 + 4*x^202 + 2*x^200 + 2*x^198 + 4*x^196 + 2*x^194 + x^192 + 4*x^190 + 2*x^188 + 3*x^186 + x^184 + x^180 + 2*x^176 + 4*x^174 + 3*x^172 + 4*x^170 + 3*x^168 + 2*x^166 + 3*x^162 + 4*x^160 + 4*x^158 + 2*x^156 + 4*x^154 + x^152 + x^150 + 4*x^148 + 2*x^146 + x^142 + x^140 + x^138 + 4*x^136 + x^134 + 2*x^132 + 4*x^130 + 3*x^128 + 3*x^126 + 2*x^124 + 4*x^120 + 3*x^118 + 3*x^116 + x^114 + 3*x^112 + x^110 + 2*x^108 + 2*x^106 + 3*x^104 + 4*x^102 + 4*x^100 + x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 4*x^84 + 4*x^82 + 4*x^78 + x^76 + 3*x^74 + 2*x^72 + 2*x^70 + 4*x^68 + x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^58 + 4*x^54 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 3*x^42 + 3*x^38 + 2*x^36 + 3*x^34 + x^32 + x^30 + 2*x^28 + 3*x^26 + 4*x^24 + x^22 + 2*x^18 + 2*x^16 + 4*x^14 + 2*x^12 + 3*x^8)*y) dx + (3*x^245 + 4*x^235 + 3*x^231 + 2*x^229 + 2*x^227 + 3*x^225 + x^223 + 2*x^221 + 4*x^219 + 4*x^215 + 4*x^205 + x^201 + 2*x^199 + 2*x^195 + 3*x^193 + 4*x^191 + 2*x^189 + 2*x^187 + x^183 + 2*x^181 + 3*x^179 + 2*x^177 + 3*x^175 + 3*x^173 + 2*x^171 + 2*x^167 + 2*x^165 + x^159 + 2*x^157 + 3*x^155 + 2*x^153 + x^151 + 3*x^149 + 4*x^147 + 4*x^145 + 2*x^143 + 4*x^141 + 2*x^139 + 3*x^133 + 3*x^131 + x^129 + 2*x^127 + 2*x^125 + 4*x^123 + 3*x^121 + x^119 + 2*x^117 + 3*x^115 + x^113 + 2*x^107 + x^105 + 2*x^101 + 4*x^99 + 2*x^97 + 2*x^95 + 2*x^93 + 4*x^91 + 2*x^89 + 3*x^87 + 3*x^85 + 4*x^83 + 4*x^81 + 4*x^79 + 3*x^77 + 4*x^75 + x^73 + 3*x^69 + 4*x^67 + 4*x^65 + 4*x^63 + 2*x^59 + 4*x^57 + 4*x^55 + x^53 + 4*x^51 + 3*x^49 + 3*x^45 + 4*x^43 + 3*x^41 + 4*x^39 + 4*x^37 + x^35 + 4*x^31 + 2*x^29 + 4*x^27 + 4*x^25 + 3*x^23 + x^21 + x^19 + 4*x^17 + 2*x^15 + 3*x^9 + 2*x^7) dy) + dV(0), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y) )
( [(3*x^11 + 2*x^7)*y] d[x] + [2*x^16 + x^12 + 2*x^8 + 3*x^6] d[y] + V(((2*x^245 + 2*x^241 + 2*x^237 + 4*x^235 + 2*x^233 + 4*x^227 + 4*x^225 + x^223 + 2*x^221 + 4*x^219 + 4*x^217 + 3*x^215 + x^211 + x^209 + 4*x^207 + 2*x^205 + 2*x^203 + 3*x^201 + 4*x^199 + 4*x^197 + 2*x^195 + 4*x^193 + 2*x^189 + x^185 + 4*x^183 + 3*x^181 + 4*x^179 + x^177 + 2*x^175 + 4*x^173 + x^163 + x^161 + 3*x^159 + 3*x^153 + 3*x^151 + 4*x^149 + 3*x^147 + 3*x^143 + 2*x^141 + 3*x^139 + 4*x^137 + 3*x^135 + 2*x^133 + 2*x^131 + 4*x^129 + 3*x^127 + 2*x^125 + 4*x^123 + 2*x^121 + 2*x^117 + 4*x^115 + 4*x^113 + x^111 + 4*x^107 + x^105 + 3*x^103 + 2*x^101 + 2*x^99 + 4*x^97 + 3*x^95 + 3*x^93 + 4*x^91 + 4*x^85 + 2*x^83 + 4*x^81 + 4*x^79 + 4*x^75 + 3*x^73 + 3*x^71 + 4*x^69 + 4*x^65 + 4*x^63 + 3*x^61 + x^59 + x^53 + x^51 + 3*x^49 + x^45 + 2*x^41 + 4*x^39 + 2*x^37 + 2*x^35 + x^33 + 4*x^29 + 4*x^27 + 2*x^25 + 3*x^23 + x^19 + x^17 + 4*x^11 + 3*x^9 + 4*x^7 + x^3)*y) dx + (3*x^250 + 3*x^240 + 3*x^236 + 2*x^234 + 2*x^232 + x^228 + x^226 + x^222 + 3*x^220 + 3*x^218 + x^216 + 2*x^214 + x^206 + 2*x^204 + 3*x^200 + 3*x^198 + x^196 + 4*x^194 + 3*x^192 + 3*x^188 + 2*x^186 + 4*x^184 + x^182 + 2*x^180 + x^174 + 4*x^172 + 4*x^170 + 2*x^168 + 3*x^166 + x^164 + x^160 + 2*x^158 + x^156 + 2*x^154 + 4*x^152 + 2*x^150 + 2*x^148 + 4*x^146 + x^144 + 2*x^142 + x^140 + 4*x^138 + 4*x^136 + 3*x^134 + x^132 + 3*x^128 + 2*x^124 + 3*x^122 + x^120 + x^114 + x^112 + 4*x^108 + x^106 + 4*x^104 + 4*x^102 + 3*x^100 + 4*x^94 + 4*x^92 + x^88 + 3*x^86 + x^84 + 2*x^82 + 2*x^80 + 2*x^78 + 2*x^76 + 3*x^74 + 4*x^72 + 3*x^70 + 2*x^66 + x^64 + 4*x^62 + 3*x^60 + 4*x^58 + 4*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + x^46 + 2*x^42 + 2*x^40 + 3*x^38 + 4*x^36 + 3*x^34 + x^28 + x^24 + x^22 + 2*x^20 + x^18 + 2*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + x^4 + 4*x^2) dy) + dV(0), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y) )
( [(4*x^18 + x^10 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [x^23 + 4*x^19 + 4*x^15 + 4*x^11 + 2*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((x^280 + x^276 + x^272 + 3*x^270 + x^268 + x^266 + 3*x^262 + x^260 + 4*x^258 + 3*x^256 + 2*x^254 + x^252 + 3*x^250 + 2*x^246 + x^242 + 4*x^236 + 4*x^234 + 4*x^232 + x^230 + 2*x^228 + 3*x^226 + 2*x^222 + 3*x^220 + x^218 + x^216 + x^214 + 3*x^212 + 4*x^210 + x^208 + x^206 + 4*x^202 + x^196 + x^194 + x^192 + 3*x^190 + 2*x^188 + x^186 + 2*x^184 + x^180 + 2*x^178 + 4*x^174 + 4*x^172 + 2*x^170 + 2*x^168 + 2*x^166 + x^164 + 2*x^162 + 3*x^160 + x^158 + x^156 + x^150 + 3*x^148 + 4*x^144 + x^142 + x^138 + 4*x^136 + 4*x^132 + 4*x^130 + 2*x^128 + x^126 + x^124 + x^122 + 3*x^120 + 3*x^118 + x^116 + 2*x^112 + 3*x^110 + x^108 + 2*x^106 + 4*x^104 + 2*x^102 + 3*x^100 + 4*x^98 + 4*x^96 + 2*x^92 + x^88 + 3*x^86 + 2*x^84 + x^82 + x^80 + 4*x^78 + 3*x^74 + 3*x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 4*x^60 + 4*x^58 + x^56 + 3*x^54 + x^48 + 3*x^46 + 2*x^44 + 4*x^42 + 3*x^40 + 4*x^38 + x^36 + 4*x^34 + 3*x^32 + 2*x^30 + 2*x^28 + 2*x^26 + 3*x^22 + 3*x^18 + 4*x^16 + 3*x^14 + 4*x^12 + x^8)*y) dx + (4*x^285 + 3*x^275 + 4*x^271 + x^269 + x^267 + 2*x^265 + 3*x^263 + 2*x^261 + x^259 + 4*x^257 + 4*x^255 + 2*x^253 + 4*x^251 + 3*x^249 + x^245 + 4*x^241 + 4*x^237 + 2*x^235 + x^233 + x^231 + 3*x^227 + x^225 + 4*x^221 + 4*x^219 + 2*x^217 + 4*x^215 + 2*x^213 + x^211 + 2*x^209 + 3*x^207 + x^203 + x^199 + 4*x^193 + x^189 + 4*x^183 + x^181 + x^179 + x^177 + x^175 + 4*x^173 + 4*x^171 + 2*x^169 + 3*x^167 + x^165 + x^163 + 2*x^161 + 2*x^159 + 3*x^157 + 3*x^155 + x^151 + 2*x^149 + 4*x^147 + 3*x^145 + 3*x^143 + 3*x^139 + 3*x^135 + 3*x^133 + 4*x^131 + 2*x^129 + 3*x^125 + 3*x^121 + x^119 + x^117 + 3*x^115 + x^113 + 3*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + 4*x^101 + 3*x^99 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 2*x^85 + x^83 + 2*x^79 + 2*x^75 + x^73 + 3*x^71 + x^69 + x^67 + 4*x^63 + x^57 + x^55 + 3*x^53 + x^51 + x^49 + 3*x^47 + x^45 + 2*x^41 + 2*x^39 + 2*x^37 + 2*x^35 + 4*x^33 + x^31 + 4*x^29 + 3*x^27 + 4*x^25 + x^23 + 2*x^21 + x^19 + 4*x^17 + 4*x^15 + x^9 + 4*x^7) dy) + dV(0), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y) )
( [(3*x^17 + 4*x^13 + 3*x^7 + x^5 + 2*x^3 + 2*x)*y] d[x] + [2*x^22 + 4*x^18 + 4*x^14 + 4*x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3] d[y] + V(((2*x^275 + 2*x^271 + 2*x^267 + 2*x^263 + x^261 + 4*x^255 + 2*x^253 + 4*x^249 + 4*x^247 + 2*x^245 + x^243 + 3*x^241 + 3*x^239 + 3*x^237 + x^235 + 2*x^233 + x^231 + 3*x^229 + x^227 + 2*x^225 + x^215 + x^213 + x^211 + 3*x^209 + x^207 + 2*x^205 + 2*x^203 + x^201 + 4*x^197 + 3*x^195 + 2*x^193 + 2*x^191 + 4*x^189 + x^187 + 4*x^185 + 4*x^183 + 3*x^181 + 4*x^179 + x^177 + 3*x^175 + x^173 + 3*x^171 + x^169 + 3*x^167 + x^165 + x^163 + 3*x^161 + 4*x^159 + 4*x^157 + 4*x^153 + 2*x^151 + 3*x^149 + 3*x^143 + 2*x^139 + 4*x^135 + 3*x^133 + 2*x^131 + 3*x^129 + 3*x^127 + x^123 + 4*x^121 + 2*x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 4*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + x^101 + 2*x^99 + 4*x^97 + 2*x^95 + 3*x^89 + x^87 + 2*x^85 + 4*x^79 + 2*x^77 + 4*x^75 + 2*x^73 + 4*x^71 + x^67 + 4*x^65 + x^61 + 4*x^59 + x^57 + 3*x^53 + 4*x^49 + 2*x^45 + 2*x^43 + 4*x^39 + 4*x^37 + 3*x^31 + 2*x^29 + 4*x^27 + 4*x^25 + 3*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^280 + 2*x^270 + 3*x^266 + 2*x^264 + 2*x^262 + x^260 + x^258 + x^254 + 2*x^252 + 4*x^250 + x^248 + x^246 + x^242 + x^240 + 3*x^238 + 2*x^236 + 4*x^234 + 2*x^230 + 3*x^228 + 4*x^226 + 3*x^222 + x^220 + 2*x^218 + 2*x^216 + x^214 + 2*x^212 + 2*x^208 + x^206 + 3*x^204 + 3*x^202 + x^194 + 4*x^192 + x^190 + 2*x^188 + 4*x^186 + 4*x^184 + x^182 + 4*x^180 + 3*x^178 + x^176 + 2*x^174 + 2*x^172 + x^166 + x^164 + 4*x^160 + 2*x^158 + x^156 + 2*x^154 + 4*x^152 + 4*x^150 + 3*x^148 + 3*x^146 + 3*x^142 + 2*x^140 + 3*x^138 + x^136 + 3*x^134 + 3*x^132 + 4*x^128 + 4*x^124 + 2*x^122 + 2*x^118 + 2*x^116 + x^114 + 3*x^112 + 2*x^110 + 4*x^108 + 4*x^106 + 3*x^104 + 2*x^102 + x^100 + 2*x^98 + 4*x^96 + 2*x^94 + 3*x^90 + 2*x^88 + 4*x^86 + x^82 + x^80 + 3*x^78 + x^76 + 4*x^74 + x^72 + 2*x^70 + x^68 + 3*x^66 + x^64 + x^62 + 3*x^60 + 4*x^58 + 4*x^54 + x^52 + 2*x^50 + 2*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + 2*x^36 + 4*x^34 + 3*x^32 + 4*x^30 + x^26 + 3*x^24 + x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y) )
( [(2*x^16 + 3*x^12 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [3*x^21 + 4*x^17 + 4*x^13 + 3*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((3*x^270 + 3*x^266 + 3*x^262 + x^260 + 3*x^258 + x^252 + x^250 + 4*x^248 + 3*x^246 + x^244 + x^242 + x^240 + 3*x^236 + 4*x^234 + 4*x^230 + 2*x^228 + x^224 + 2*x^222 + 3*x^220 + x^218 + x^214 + x^208 + 4*x^206 + 4*x^204 + 2*x^202 + 3*x^200 + 4*x^196 + 4*x^194 + 3*x^192 + x^190 + 4*x^188 + x^186 + 4*x^184 + 3*x^182 + 4*x^180 + x^178 + x^174 + 4*x^170 + 4*x^168 + 2*x^164 + x^162 + 4*x^160 + 2*x^156 + 2*x^152 + 3*x^150 + 4*x^148 + 2*x^142 + x^138 + 2*x^136 + 3*x^134 + x^132 + 4*x^130 + 2*x^128 + 2*x^124 + 3*x^122 + 3*x^120 + 3*x^118 + 3*x^116 + 3*x^114 + 2*x^112 + 4*x^106 + 4*x^104 + 3*x^102 + 2*x^96 + x^94 + 3*x^92 + 3*x^90 + 3*x^86 + 4*x^84 + 3*x^82 + 3*x^80 + 3*x^76 + 4*x^74 + 2*x^72 + 2*x^70 + 2*x^68 + x^66 + 4*x^64 + 4*x^62 + x^60 + 3*x^58 + x^56 + 3*x^54 + x^50 + 4*x^44 + 4*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^30 + 2*x^26 + 3*x^22 + 3*x^18 + 4*x^16 + 3*x^14 + 4*x^12 + x^8)*y) dx + (2*x^275 + 2*x^265 + 2*x^261 + 3*x^259 + 3*x^257 + 4*x^253 + 4*x^251 + 4*x^247 + 3*x^245 + 2*x^243 + 4*x^241 + 3*x^239 + 3*x^235 + 2*x^229 + 4*x^227 + 3*x^225 + 4*x^223 + 3*x^221 + 4*x^219 + 2*x^217 + 3*x^215 + 2*x^213 + 3*x^211 + x^209 + 4*x^207 + 2*x^201 + 3*x^199 + x^197 + 3*x^195 + 4*x^193 + 4*x^191 + 4*x^189 + 3*x^183 + 4*x^177 + x^175 + x^173 + 3*x^171 + 3*x^169 + 3*x^167 + 3*x^165 + 4*x^163 + 2*x^161 + x^157 + x^155 + 4*x^153 + 4*x^151 + x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 2*x^137 + x^135 + x^133 + 3*x^131 + 2*x^127 + 3*x^125 + 2*x^123 + 4*x^121 + 4*x^119 + 3*x^117 + 2*x^113 + x^111 + 4*x^109 + 3*x^107 + 2*x^105 + 4*x^97 + 4*x^95 + 3*x^93 + 3*x^91 + 2*x^89 + x^87 + 4*x^83 + 2*x^81 + x^79 + x^77 + 2*x^71 + 2*x^69 + 4*x^65 + x^63 + 2*x^61 + 4*x^59 + 2*x^57 + 2*x^55 + 4*x^53 + 2*x^51 + 3*x^49 + 2*x^47 + 4*x^45 + 3*x^43 + 3*x^41 + 4*x^39 + 4*x^35 + 4*x^33 + x^31 + 2*x^29 + 4*x^25 + x^23 + 2*x^21 + x^19 + 4*x^17 + 4*x^15 + x^9 + 4*x^7) dy) + dV(0), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y) )
( [(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x)*y] d[x] + [4*x^20 + 4*x^16 + 4*x^12 + 4*x^8 + 4*x^4 + 1] d[y] + V(((4*x^265 + 4*x^261 + 4*x^257 + x^255 + 4*x^253 + 3*x^251 + x^247 + 2*x^245 + 2*x^241 + 3*x^239 + 2*x^237 + 3*x^235 + 2*x^233 + 3*x^229 + 3*x^223 + x^221 + 3*x^219 + 3*x^217 + x^215 + 4*x^213 + 2*x^211 + 4*x^209 + 4*x^207 + 2*x^205 + 2*x^203 + 2*x^201 + 3*x^199 + 2*x^197 + 3*x^195 + 4*x^193 + 3*x^191 + x^185 + x^183 + 3*x^181 + 3*x^179 + 4*x^177 + x^175 + 4*x^173 + x^165 + 2*x^163 + 3*x^161 + 2*x^159 + 4*x^157 + x^153 + x^151 + 4*x^149 + 4*x^147 + x^145 + 2*x^143 + 3*x^141 + 2*x^139 + 4*x^137 + 4*x^133 + 2*x^131 + 4*x^129 + 3*x^127 + 4*x^123 + 2*x^121 + 3*x^119 + 3*x^117 + x^115 + x^113 + 4*x^111 + 4*x^103 + 4*x^101 + x^99 + 2*x^97 + x^95 + 3*x^93 + x^91 + x^89 + 3*x^87 + 3*x^85 + 2*x^81 + 2*x^77 + 3*x^75 + 3*x^73 + 3*x^71 + 3*x^67 + 2*x^65 + 3*x^61 + 2*x^59 + 3*x^57 + 2*x^55 + 4*x^53 + x^51 + 3*x^47 + 3*x^45 + 2*x^43 + 2*x^41 + 2*x^39 + 3*x^35 + x^31 + 4*x^27 + x^25 + 3*x^23 + 4*x^21 + x^19 + 2*x^17 + x^13 + 2*x^11 + 4*x^9 + 2*x^7 + 3*x^3)*y) dx + (x^270 + 3*x^260 + x^256 + 4*x^254 + 4*x^252 + 4*x^250 + 2*x^248 + 4*x^246 + 3*x^244 + 3*x^240 + 3*x^236 + 2*x^234 + 2*x^232 + 4*x^230 + x^228 + 2*x^224 + 4*x^222 + 4*x^220 + 3*x^218 + 2*x^216 + 2*x^214 + 4*x^212 + 2*x^208 + 3*x^204 + 4*x^202 + x^200 + 4*x^198 + 3*x^196 + 3*x^194 + 3*x^192 + x^190 + 3*x^188 + 3*x^186 + 2*x^184 + 4*x^182 + 2*x^180 + x^178 + 4*x^176 + 3*x^174 + 2*x^172 + 4*x^170 + 4*x^168 + 3*x^166 + x^164 + 4*x^162 + 4*x^160 + 4*x^156 + x^154 + x^152 + 2*x^150 + 2*x^148 + 3*x^146 + 4*x^144 + 3*x^142 + 2*x^140 + x^138 + x^136 + 3*x^134 + x^132 + 2*x^130 + 3*x^126 + x^124 + 2*x^122 + 2*x^120 + 4*x^118 + 4*x^116 + x^114 + 4*x^112 + x^110 + 2*x^108 + x^106 + 4*x^104 + 2*x^102 + x^100 + 3*x^98 + 2*x^94 + 4*x^90 + 3*x^88 + 3*x^86 + x^84 + x^80 + 4*x^78 + x^76 + 3*x^74 + 3*x^72 + x^70 + 4*x^68 + 4*x^64 + 4*x^62 + 3*x^60 + 3*x^58 + 2*x^56 + 2*x^52 + 4*x^48 + 3*x^44 + 4*x^42 + 4*x^38 + x^34 + 3*x^30 + 4*x^28 + 2*x^26 + x^22 + 3*x^18 + x^16 + 2*x^10 + 3*x^4 + 2*x^2) dy) + dV(0), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y) )
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:28, in <module>

File <string>:92, in regular_drw_cech(cocycle)

File <string>:81, in regular_drw_form(omega)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
   1962         return y
   1963 
-> 1964     return coercion_model.bin_op(left, right, operator.mul)
   1965 
   1966 cpdef _mul_(self, right):

File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:95, in diffn(self)

File <string>:7, in __init__(self, C, g)

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    112 FieldElement.__init__(self, parent)
    113 if coerce:
--> 114     self.__numerator   = parent.ring()(numerator)
    115     self.__denominator = parent.ring()(denominator)
    116 else:

File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
    895 if mor is not None:
    896     if no_extra_args:
--> 897         return mor._call_(x)
    898     else:
    899         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
   1001 
   1002         try:
-> 1003             return self(str(element))
   1004         except TypeError:
   1005             pass

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:482, in sage.rings.fraction_field_element.FractionFieldElement._repr_()
    480 if self.is_zero():
    481     return "0"
--> 482 s = "%s" % self.__numerator
    483 if self.__denominator != 1:
    484     denom_string = str( self.__denominator )

File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    192 except AttributeError:
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):
    196     return result

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
   2689     """
-> 2690     return self._repr()
   2691 
   2692 def _latex_(self, name=None):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
   2654 if n != m-1:
   2655     s += " + "
-> 2656 x = y = repr(x)
   2657 if y.find("-") == 0:
   2658     y = y[1:]

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Input In [3] in <cell line: 1>
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:21 in <module>

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:40
    C = omega.curve
    ^
IndentationError: unexpected indent

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32, in <module>

File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:25, in <module>

File <string>:92, in regular_drw_cech(cocycle)

File <string>:84, in regular_drw_form(omega)

File <string>:5, in decomposition_g0_pth_power(fct)

AttributeError: 'superelliptic_function' object has no attribute 'fucntion'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(elliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/superelliptic_drw_auxilliaries.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in itertools.product(*lista):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lbB1:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for b in B:

....: [?7h[?12l[?25h[?25l[?7lp = C.characteristic[?7h[?12l[?25h[?25l[?7lrint(b.regula_form())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(b.regular_form())[?7h[?12l[?25h[?25l[?7l....:     print(b.regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in B:

....:     print(b.regular_form())

....: 

[?7h[?12l[?25h[?2004l( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in B:

....:     print(b.regular_form())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(b.regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in B1:

....:     print(b.regular_form())

....: 

[?7h[?12l[?25h[?2004l( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((x^99 + 2*x^91 + 3*x^89 + 3*x^87 + 2*x^85 + 2*x^83 + 2*x^79 + x^77 + 4*x^75 + x^73 + 2*x^71 + 2*x^69 + 3*x^67 + 3*x^65 + x^63 + 3*x^61 + x^55 + 2*x^53 + 4*x^51 + x^49 + 2*x^47 + 4*x^45 + 4*x^43 + 3*x^35 + 2*x^33 + 2*x^31 + 2*x^29 + 3*x^25 + x^23 + 3*x^21 + 3*x^19 + 3*x^15 + x^13 + 4*x^11 + 2*x^7 + 4*x^5 + x^3 + 3*x)*y) dx + (4*x^104 + x^100 + 3*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + x^88 + 3*x^84 + 3*x^80 + 3*x^78 + 2*x^76 + 4*x^74 + 3*x^70 + 4*x^68 + x^66 + 2*x^62 + x^60 + 3*x^58 + 2*x^56 + x^54 + 2*x^52 + 3*x^50 + 4*x^46 + 2*x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + 4*x^32 + 3*x^30 + 3*x^28 + x^26 + 4*x^24 + 4*x^22 + 4*x^20 + x^18 + x^16 + x^14 + 4*x^12 + 4*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) )
( [(3*x^6 + 2*x^2)*y] d[x] + [2*x^11 + x^7 + 2*x^3 + 3*x] d[y] + V(((x^104 + x^100 + x^94 + x^90 + x^88 + 4*x^86 + x^84 + x^82 + 4*x^80 + 4*x^78 + 4*x^76 + x^74 + 4*x^72 + 2*x^70 + 2*x^66 + 4*x^64 + 2*x^60 + 4*x^58 + 3*x^56 + 3*x^54 + 4*x^52 + 2*x^50 + 4*x^48 + x^44 + 2*x^42 + 3*x^40 + 3*x^38 + 3*x^36 + 4*x^34 + x^32 + 3*x^30 + 3*x^28 + 4*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 4*x^18 + x^16 + 2*x^14 + 4*x^12 + 4*x^10 + 4*x^8 + x^4 + 2*x^2)*y) dx + (4*x^109 + x^101 + 2*x^95 + 4*x^93 + 4*x^91 + x^89 + 4*x^85 + x^81 + 2*x^79 + 2*x^77 + 2*x^75 + 2*x^71 + 3*x^69 + 3*x^67 + x^65 + 2*x^63 + x^59 + 3*x^55 + 2*x^51 + x^49 + 2*x^47 + 3*x^45 + 2*x^43 + 3*x^39 + 4*x^37 + 3*x^35 + 3*x^33 + 4*x^31 + 3*x^29 + 3*x^27 + 4*x^25 + 2*x^23 + 2*x^21 + 3*x^15 + 2*x^13 + 2*x^9 + 3*x^7 + 4*x^5 + x^3 + 3*x) dy) + dV(0), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y) )
( [(3*x^7 + 2*x^3)*y] d[x] + [2*x^12 + x^8 + 2*x^4 + 3*x^2] d[y] + V(((x^109 + 2*x^105 + 3*x^101 + 4*x^99 + 2*x^97 + 3*x^91 + x^87 + 4*x^85 + 2*x^83 + x^81 + x^75 + 4*x^73 + x^71 + 3*x^69 + 3*x^65 + x^63 + 2*x^61 + x^57 + 4*x^53 + 2*x^49 + 4*x^47 + 3*x^45 + 4*x^43 + 4*x^41 + x^39 + 2*x^37 + 3*x^35 + 4*x^27 + x^25 + 2*x^23 + 3*x^21 + 4*x^19 + x^17 + 4*x^15 + 3*x^13 + x^11 + 2*x^7 + 2*x^5 + 3*x^3 + 4*x)*y) dx + (4*x^114 + 4*x^110 + 4*x^106 + 2*x^104 + x^102 + 2*x^100 + 2*x^98 + 3*x^96 + 4*x^94 + 2*x^88 + 4*x^82 + x^80 + x^78 + 3*x^76 + x^74 + 4*x^72 + x^70 + x^68 + 3*x^66 + x^64 + 3*x^62 + 3*x^60 + 2*x^52 + 2*x^50 + 2*x^46 + 4*x^42 + 3*x^40 + 3*x^38 + 2*x^36 + 2*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + 3*x^26 + 4*x^24 + x^22 + 2*x^20 + 4*x^18 + 3*x^16 + 3*x^14 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + x^2 + 1) dy) + dV(0), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y) )
( [(3*x^8 + 2*x^4)*y] d[x] + [2*x^13 + x^9 + 2*x^5 + 3*x^3] d[y] + V(((x^114 + 3*x^110 + x^106 + 2*x^104 + 4*x^102 + 4*x^100 + 4*x^98 + 2*x^96 + 4*x^94 + x^92 + 4*x^90 + 3*x^86 + 4*x^84 + x^82 + 3*x^78 + 2*x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + 3*x^62 + 3*x^60 + 4*x^58 + 3*x^54 + x^52 + 3*x^50 + 3*x^44 + 3*x^42 + 3*x^40 + 2*x^38 + x^36 + x^34 + x^32 + x^24 + 3*x^22 + 4*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + 2*x^12 + 4*x^10 + x^8 + x^6 + 4*x^2)*y) dx + (4*x^119 + 3*x^115 + 2*x^111 + 4*x^109 + 2*x^107 + 2*x^105 + 2*x^101 + 2*x^99 + x^95 + 4*x^93 + 4*x^91 + 3*x^89 + x^87 + 2*x^83 + 4*x^81 + 4*x^79 + x^75 + x^71 + x^69 + x^67 + 3*x^65 + 3*x^61 + 4*x^59 + 2*x^57 + x^55 + 3*x^53 + 4*x^51 + 2*x^49 + 4*x^47 + 3*x^45 + 3*x^43 + x^39 + x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^29 + 2*x^27 + x^25 + x^23 + x^21 + x^19 + 2*x^17 + 3*x^15 + 2*x^9 + x^7 + 4*x^3 + x) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y) )
( [(3*x^9 + 2*x^5)*y] d[x] + [2*x^14 + x^10 + 2*x^6 + 3*x^4] d[y] + V(((x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^83 + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 + 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x)*y) dx + (4*x^124 + 2*x^120 + x^114 + 3*x^112 + 2*x^110 + 3*x^108 + x^106 + 2*x^100 + x^98 + 3*x^96 + x^94 + 3*x^92 + 4*x^90 + 3*x^88 + 2*x^84 + x^82 + x^80 + 4*x^78 + 4*x^76 + x^74 + 4*x^72 + 3*x^70 + x^66 + 3*x^64 + 2*x^62 + x^58 + x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 4*x^40 + 2*x^34 + 3*x^32 + 3*x^28 + 4*x^26 + 4*x^24 + 4*x^22 + 4*x^20 + 2*x^14 + 4*x^10 + 3*x^8 + 2*x^6 + 4*x^4 + 4*x^2 + 1) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y) )
( [(3*x^10 + 2*x^6)*y] d[x] + [2*x^15 + x^11 + 2*x^7 + 3*x^5] d[y] + V(((x^124 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^110 + 2*x^108 + 2*x^104 + x^102 + 4*x^100 + x^98 + 2*x^96 + 2*x^94 + 3*x^92 + 3*x^90 + x^88 + 3*x^86 + x^80 + 2*x^78 + 4*x^76 + x^74 + 2*x^72 + 4*x^70 + 4*x^68 + 3*x^60 + 2*x^58 + 2*x^56 + 2*x^54 + 3*x^50 + x^48 + 3*x^46 + 3*x^44 + 3*x^40 + x^38 + 4*x^36 + 2*x^32 + 4*x^30 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + x^18 + 4*x^16 + 4*x^14 + 3*x^12 + 2*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 3*x^2)*y) dx + (4*x^129 + x^125 + 3*x^121 + 3*x^119 + 4*x^117 + 2*x^115 + x^113 + 3*x^109 + 3*x^105 + 3*x^103 + 2*x^101 + 4*x^99 + 3*x^95 + 4*x^93 + x^91 + 2*x^87 + x^85 + 3*x^83 + 2*x^81 + x^79 + 2*x^77 + 3*x^75 + 4*x^71 + 2*x^69 + 2*x^67 + 4*x^65 + 4*x^63 + 3*x^61 + x^59 + 4*x^57 + 3*x^55 + 3*x^53 + x^51 + 4*x^49 + 4*x^47 + 4*x^45 + x^43 + x^41 + x^39 + 4*x^37 + 4*x^35 + 2*x^31 + 2*x^29 + x^27 + 2*x^19 + 4*x^17 + 2*x^11 + 2*x^9 + 4*x^7 + 3*x^5 + 2*x) dy) + dV(0), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y) )
( [(3*x^11 + 2*x^7)*y] d[x] + [2*x^16 + x^12 + 2*x^8 + 3*x^6] d[y] + V(((x^129 + x^125 + x^119 + x^115 + x^113 + 4*x^111 + x^109 + x^107 + 4*x^105 + 4*x^103 + 4*x^101 + x^99 + 4*x^97 + 2*x^95 + 2*x^91 + 4*x^89 + 2*x^85 + 4*x^83 + 3*x^81 + 3*x^79 + 4*x^77 + 2*x^75 + 4*x^73 + x^69 + 2*x^67 + 3*x^65 + 3*x^63 + 3*x^61 + 4*x^59 + x^57 + 3*x^55 + 3*x^53 + 4*x^51 + 4*x^49 + 2*x^47 + 2*x^45 + 4*x^43 + x^41 + 2*x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 3*x^29 + 2*x^27 + x^23 + 3*x^21 + x^19 + 2*x^15 + x^13 + x^9 + x^7 + 3*x)*y) dx + (4*x^134 + x^126 + 2*x^120 + 4*x^118 + 4*x^116 + x^114 + 4*x^110 + x^106 + 2*x^104 + 2*x^102 + 2*x^100 + 2*x^96 + 3*x^94 + 3*x^92 + x^90 + 2*x^88 + x^84 + 3*x^80 + 2*x^76 + x^74 + 2*x^72 + 3*x^70 + 2*x^68 + 3*x^64 + 4*x^62 + 3*x^60 + 3*x^58 + 4*x^56 + 3*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + 2*x^46 + 3*x^40 + 2*x^38 + 3*x^32 + x^30 + 2*x^24 + 3*x^22 + x^20 + 2*x^16 + 2*x^14 + 4*x^12 + 2*x^8 + x^6 + 2*x^4 + 3*x^2 + 2) dy) + dV(0), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y) )
( [(4*x^18 + x^10 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [x^23 + 4*x^19 + 4*x^15 + 4*x^11 + 2*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((3*x^164 + 4*x^160 + x^156 + x^154 + 3*x^152 + x^150 + 4*x^148 + x^146 + 2*x^144 + 3*x^140 + 2*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + 2*x^126 + 4*x^124 + 4*x^122 + 2*x^120 + 3*x^118 + 4*x^116 + 4*x^114 + 2*x^110 + x^108 + 4*x^106 + 2*x^100 + 2*x^98 + 2*x^96 + x^94 + 3*x^92 + 2*x^90 + 4*x^88 + x^86 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^78 + 3*x^72 + x^70 + x^68 + x^64 + x^60 + x^58 + 2*x^56 + 2*x^54 + 3*x^52 + 3*x^50 + x^48 + 3*x^46 + 3*x^44 + x^40 + 4*x^36 + 3*x^34 + 3*x^32 + 3*x^30 + x^28 + 4*x^26 + 2*x^24 + 3*x^22 + 2*x^20 + x^18 + 4*x^16 + 2*x^12 + 2*x^10 + x^6 + 2*x^4 + x^2)*y) dx + (2*x^169 + 4*x^165 + 3*x^161 + 2*x^159 + 3*x^157 + 2*x^155 + 4*x^153 + 3*x^151 + 3*x^149 + 2*x^147 + x^145 + 3*x^143 + x^141 + 3*x^139 + x^137 + 4*x^135 + 4*x^129 + 3*x^121 + 2*x^119 + 3*x^117 + 2*x^115 + x^113 + 2*x^111 + 2*x^109 + 3*x^107 + x^105 + 3*x^103 + 2*x^101 + x^99 + x^97 + x^95 + 3*x^93 + x^87 + 2*x^85 + x^83 + 2*x^81 + 2*x^79 + 2*x^77 + 3*x^75 + 4*x^73 + 2*x^69 + 2*x^67 + 3*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 2*x^57 + 4*x^55 + x^53 + 2*x^51 + 4*x^49 + 3*x^47 + x^45 + x^43 + 4*x^41 + x^39 + 3*x^37 + 4*x^33 + 3*x^31 + 4*x^29 + 3*x^27 + 3*x^25 + x^19 + 2*x^17 + 3*x^13 + 2*x^11 + 4*x^9 + 3*x^7 + 4*x^3 + 4*x) dy) + dV(0), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y) )
( [(3*x^17 + 4*x^13 + 3*x^7 + x^5 + 2*x^3 + 2*x)*y] d[x] + [2*x^22 + 4*x^18 + 4*x^14 + 4*x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3] d[y] + V(((x^159 + 2*x^155 + 2*x^151 + 4*x^149 + x^147 + 2*x^145 + 3*x^143 + x^141 + 3*x^139 + 4*x^137 + 2*x^135 + 2*x^133 + x^131 + x^129 + 4*x^127 + x^125 + 3*x^123 + 2*x^121 + 3*x^119 + 3*x^115 + 2*x^111 + 3*x^107 + 4*x^103 + 2*x^101 + 2*x^99 + 3*x^97 + 4*x^95 + 3*x^93 + 4*x^91 + x^89 + 4*x^87 + 4*x^85 + x^83 + 2*x^77 + 2*x^69 + 3*x^67 + 3*x^63 + 4*x^61 + 4*x^59 + x^55 + 3*x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 3*x^41 + 2*x^39 + x^37 + 2*x^33 + 2*x^31 + x^29 + 4*x^27 + x^25 + 2*x^23 + x^19 + 4*x^17 + x^15 + x^13 + 4*x^11 + 4*x^7 + x^5 + 3*x^3 + 2*x)*y) dx + (4*x^164 + 4*x^160 + 2*x^154 + x^152 + 3*x^148 + x^146 + 4*x^144 + 3*x^142 + 2*x^140 + x^138 + 3*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 4*x^126 + 4*x^124 + x^122 + 2*x^118 + 3*x^116 + x^112 + 3*x^110 + x^108 + 3*x^106 + 4*x^104 + 2*x^102 + 2*x^98 + 4*x^96 + x^94 + 2*x^92 + 3*x^88 + x^86 + 2*x^84 + 4*x^82 + 4*x^78 + 4*x^72 + 4*x^70 + 2*x^68 + 3*x^66 + 3*x^64 + 4*x^62 + 2*x^60 + 3*x^56 + x^48 + 4*x^46 + 3*x^44 + x^40 + x^38 + x^32 + 4*x^30 + 2*x^28 + 2*x^26 + 2*x^24 + x^22 + 2*x^20 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 3*x^8 + 2*x^6 + 4*x^2 + 3) dy) + dV(0), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y) )
( [(2*x^16 + 3*x^12 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [3*x^21 + 4*x^17 + 4*x^13 + 3*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((4*x^154 + 4*x^150 + 4*x^144 + x^142 + 4*x^140 + 2*x^138 + 4*x^136 + 4*x^134 + 2*x^132 + 4*x^130 + x^128 + 2*x^126 + 3*x^124 + 2*x^122 + 3*x^120 + 3*x^116 + 4*x^114 + 3*x^112 + x^106 + 3*x^104 + 3*x^102 + 2*x^98 + 3*x^96 + 4*x^94 + x^92 + 4*x^88 + 4*x^84 + x^80 + x^78 + 4*x^74 + 3*x^72 + 2*x^70 + 2*x^68 + 3*x^66 + x^64 + 4*x^62 + 3*x^60 + 4*x^56 + 3*x^54 + 3*x^50 + 4*x^48 + 3*x^46 + 4*x^42 + 2*x^38 + 4*x^36 + 3*x^34 + 4*x^32 + 2*x^28 + 3*x^26 + 2*x^20 + 2*x^16 + 3*x^14 + 3*x^10 + 2*x^8 + 2*x^6 + 4*x^4)*y) dx + (x^159 + 4*x^151 + 4*x^147 + 3*x^145 + 4*x^143 + 3*x^141 + 2*x^139 + x^137 + 3*x^135 + 2*x^133 + 4*x^131 + 3*x^129 + 4*x^127 + 4*x^125 + 2*x^123 + x^121 + 4*x^119 + 3*x^117 + x^113 + 3*x^111 + 4*x^109 + 3*x^103 + 3*x^99 + 3*x^97 + 4*x^95 + 3*x^91 + 2*x^89 + 4*x^87 + 2*x^83 + 3*x^81 + 4*x^79 + 4*x^77 + 4*x^73 + 2*x^71 + 3*x^69 + 2*x^65 + 2*x^63 + x^61 + x^59 + 2*x^55 + 2*x^53 + x^51 + 3*x^49 + 2*x^45 + 2*x^43 + x^41 + 4*x^39 + 4*x^37 + 3*x^35 + 3*x^33 + x^31 + x^29 + x^27 + 2*x^25 + 2*x^21 + 2*x^19 + 4*x^17 + 2*x^15 + 3*x^9 + x^7 + 2*x^5 + x^3) dy) + dV(0), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y) )
( [(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x)*y] d[x] + [4*x^20 + 4*x^16 + 4*x^12 + 4*x^8 + 4*x^4 + 1] d[y] + V(((2*x^149 + x^139 + 2*x^135 + x^131 + 2*x^127 + 4*x^125 + x^123 + x^121 + 3*x^119 + x^117 + 2*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + 2*x^101 + 3*x^99 + 4*x^97 + 2*x^95 + 3*x^93 + 2*x^89 + 3*x^83 + x^81 + x^79 + 2*x^77 + 3*x^73 + 3*x^71 + 2*x^69 + x^67 + 2*x^63 + 3*x^61 + 4*x^59 + 2*x^57 + 3*x^55 + 4*x^53 + 4*x^51 + x^47 + 2*x^45 + 2*x^43 + 3*x^37 + x^35 + 4*x^33 + 2*x^31 + 2*x^29 + 3*x^27 + x^25 + 4*x^23 + 2*x^21 + 4*x^19 + 2*x^17 + 3*x^15 + 3*x^13 + 3*x^11 + x^9 + 2*x^3 + 3*x)*y) dx + (3*x^154 + 2*x^150 + x^144 + x^140 + 3*x^136 + x^134 + x^132 + 4*x^130 + 3*x^128 + 2*x^126 + x^122 + 4*x^120 + 3*x^118 + 3*x^114 + x^112 + 3*x^110 + 4*x^108 + 4*x^106 + 4*x^102 + 3*x^96 + 3*x^94 + x^90 + 3*x^86 + 2*x^84 + 3*x^82 + x^80 + x^78 + 3*x^76 + 4*x^74 + 3*x^66 + x^64 + 3*x^62 + 4*x^60 + 2*x^58 + 2*x^54 + x^52 + 4*x^50 + x^48 + 2*x^46 + 4*x^44 + 3*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + x^32 + 3*x^24 + 4*x^22 + 2*x^18 + x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 4*x^4 + x^2 + 2) dy) + dV(0), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y) )
( [(x^10 + 2*x^6 + 2*x^2)*y] d[x] + [4*x^15 + 4*x^11 + x^5 + 2*x^3 + 3*x] d[y] + V(((2*x^124 + x^114 + x^112 + 2*x^110 + x^108 + 3*x^104 + x^102 + 3*x^100 + 4*x^96 + x^94 + x^92 + 4*x^90 + 4*x^86 + 3*x^82 + 3*x^80 + 4*x^78 + 3*x^74 + 2*x^72 + 3*x^70 + 4*x^68 + 2*x^66 + 2*x^64 + 4*x^60 + 3*x^58 + x^54 + 4*x^52 + 2*x^48 + 4*x^42 + x^40 + 3*x^36 + 3*x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 2*x^20 + 4*x^18 + 3*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + 3*x^8 + 3*x^6 + 2*x^2)*y) dx + (3*x^129 + 2*x^125 + x^119 + 4*x^117 + x^115 + 4*x^111 + 4*x^109 + 2*x^107 + 3*x^105 + 2*x^101 + x^99 + 2*x^97 + 2*x^95 + 4*x^91 + x^87 + x^85 + 4*x^83 + x^81 + x^79 + 4*x^77 + 3*x^75 + 3*x^73 + 4*x^71 + 2*x^67 + 4*x^65 + x^63 + 2*x^61 + 3*x^59 + 4*x^57 + x^55 + 3*x^53 + 4*x^49 + x^45 + x^39 + 4*x^37 + 2*x^35 + 3*x^33 + x^31 + 2*x^29 + x^25 + 3*x^23 + 4*x^21 + x^19 + x^15 + 2*x^13 + x^11 + 4*x^9 + 3*x^7 + 2*x^3 + 3*x) dy) + dV(0), [2/x^5*y] + V(((4*x^106 + 3*x^102 + 2*x^100 + x^98 + 3*x^94 + 4*x^92 + 3*x^90 + x^86 + 2*x^84 + 3*x^80 + 4*x^78 + 2*x^76 + x^72 + 2*x^68 + 2*x^66 + 4*x^64 + 4*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + 3*x^46 + x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + x^32 + 3*x^30 + x^24 + 3*x^22 + 2*x^20 + 2*x^18 + x^16 + x^12 + 3*x^8 + x^6 + 4)/x^5)*y) )
( [(4*x^13 + x^5)*y] d[x] + [x^18 + 4*x^14 + 4*x^10 + 4*x^8 + x^6 + 4*x^4] d[y] + V(((3*x^139 + 4*x^135 + x^131 + x^129 + 3*x^127 + x^125 + 2*x^123 + 4*x^121 + 2*x^119 + 2*x^117 + x^115 + x^113 + x^109 + 2*x^107 + 3*x^103 + 2*x^101 + x^97 + x^95 + x^93 + 3*x^91 + x^89 + 4*x^87 + 4*x^85 + 3*x^83 + x^81 + 4*x^77 + x^75 + 4*x^73 + x^71 + 4*x^69 + x^65 + 4*x^61 + x^59 + 3*x^57 + x^55 + 4*x^49 + 2*x^47 + x^45 + 2*x^43 + 4*x^41 + 2*x^39 + 3*x^35 + 3*x^33 + 2*x^29 + 2*x^27 + x^25 + 4*x^23 + x^21 + 2*x^17 + 2*x^15 + 4*x^13 + x^11 + 2*x^7 + x^5 + 4*x^3 + 2*x)*y) dx + (2*x^144 + 4*x^140 + 3*x^136 + 2*x^134 + 3*x^132 + 2*x^130 + x^128 + x^124 + 3*x^122 + 3*x^120 + 4*x^118 + 2*x^116 + x^112 + 2*x^110 + 3*x^108 + 4*x^106 + 3*x^104 + 4*x^102 + 4*x^100 + x^98 + x^94 + 2*x^92 + 4*x^90 + 3*x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 2*x^74 + x^70 + 3*x^68 + x^66 + x^64 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 3*x^52 + 4*x^50 + 3*x^46 + 4*x^44 + 2*x^42 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 2*x^32 + x^30 + 3*x^24 + x^22 + 3*x^20 + 4*x^18 + 2*x^16 + 2*x^12 + 2*x^10 + 3*x^6 + x^4 + 3*x^2 + 3) dy) + dV(0), [2/x^6*y] + V(((x^120 + 2*x^116 + 3*x^114 + 4*x^112 + 2*x^108 + x^106 + 2*x^104 + 2*x^100 + 3*x^98 + x^96 + x^94 + 3*x^92 + 3*x^90 + x^88 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^76 + x^74 + x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 2*x^60 + 4*x^52 + x^50 + x^48 + 2*x^46 + 2*x^44 + x^40 + 3*x^38 + 4*x^34 + 2*x^32 + 3*x^30 + x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 3*x^16 + x^14 + 4*x^12 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + 2)/x^4)*y) )
( [(3*x^12 + 4*x^8 + 3*x^4)*y] d[x] + [2*x^17 + 4*x^13 + x^9 + 3*x^7 + 3*x^5 + 2*x^3] d[y] + V(((x^134 + 2*x^130 + 2*x^126 + 4*x^124 + 3*x^122 + 2*x^120 + 4*x^118 + x^116 + 4*x^114 + 3*x^110 + x^108 + 2*x^104 + x^102 + x^100 + 3*x^98 + 3*x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 4*x^88 + 4*x^86 + x^84 + 2*x^82 + 2*x^80 + 3*x^76 + 3*x^74 + 2*x^72 + 2*x^70 + 4*x^68 + 3*x^64 + 2*x^62 + 3*x^58 + 3*x^54 + 4*x^52 + 3*x^50 + 2*x^48 + 4*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + 2*x^34 + 2*x^30 + 3*x^28 + 2*x^26 + x^24 + 2*x^22 + 3*x^18 + 4*x^16 + 4*x^14 + 2*x^12 + 3*x^10 + x^8 + x^2)*y) dx + (4*x^139 + 4*x^135 + 2*x^129 + 4*x^127 + 4*x^123 + x^121 + 4*x^119 + 4*x^117 + 2*x^115 + x^113 + x^107 + x^103 + 2*x^101 + x^99 + 4*x^97 + 3*x^93 + 3*x^91 + 3*x^89 + 2*x^85 + 4*x^83 + x^81 + x^75 + 2*x^73 + 3*x^69 + 3*x^67 + 2*x^65 + 3*x^63 + 4*x^61 + 2*x^59 + 2*x^57 + 2*x^55 + x^53 + 4*x^49 + 2*x^47 + 2*x^45 + 3*x^39 + 2*x^37 + x^35 + 3*x^33 + 4*x^31 + 4*x^27 + x^25 + x^23 + 3*x^21 + 2*x^19 + x^17 + 4*x^15 + 3*x^13 + 2*x^9 + 3*x^7 + 4*x^5 + x^3 + 4*x) dy) + dV(0), [2/x^7*y] + V(((2*x^118 + 4*x^114 + x^112 + 3*x^110 + 4*x^106 + 2*x^104 + 4*x^102 + x^96 + 4*x^94 + x^88 + 4*x^86 + 4*x^82 + x^80 + 3*x^78 + 3*x^76 + 4*x^70 + 2*x^62 + 4*x^60 + 4*x^58 + 2*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + x^46 + 4*x^42 + 4*x^38 + 4*x^36 + x^34 + 2*x^30 + 4*x^28 + 4*x^26 + 4*x^22 + 4*x^20 + 2*x^18 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 3*x^2 + 2)/x^7)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, (1/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((x/y) dx, 0, (x/y) dx),
 ((x^2/y) dx, 0, (x^2/y) dx),
 ((x^3/y) dx, 0, (x^3/y) dx),
 ((x^4/y) dx, 0, (x^4/y) dx),
 ((x^5/y) dx, 0, (x^5/y) dx),
 ((x^6/y) dx, 0, (x^6/y) dx),
 (((-2*x^13 - 2*x^9 - 2*x^3 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx),
 (((x^12 - x^8 - x^4 + x^2 + 1)/y) dx, 2/x^2*y, (2/(x^2*y)) dx),
 (((-x^11 - 2*x^3 - x)/y) dx, 2/x^3*y, (2/(x*y)) dx),
 (((2*x^10 + x^6 + 2*x^2 + 2)/y) dx, 2/x^4*y, ((-2)/(x^4*y)) dx),
 (((2*x^5 + x)/y) dx, 2/x^5*y, ((-2*x^2 + 1)/(x^5*y)) dx),
 (((-2*x^8 - 2*x^4)/y) dx, 2/x^6*y, ((2*x^4 + x^2 - 1)/(x^6*y)) dx),
 (((x^7 - x^3)/y) dx, 2/x^7*y, ((x^6 - x^4 - x^2 + 2)/(x^7*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""n"a"p"r"a"w"i"o"n"e" "r"e"g"u"l"a"r" "f"o"r"m";" "s"u"p"e"r"e"l"l"i"p"t"y"c"z"n"e" "m"a"j"a" "C"."x"_"s"e"r"i"e"s" "i"t"d"
[master 64fe2ee] naprawione regular form; superelliptyczne maja C.x_series itd
 10 files changed, 20233 insertions(+), 46862 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': 3Cardano
Password for 'https://3Cardano@git.wmi.amu.edu.pl': 
remote: Unauthorized
fatal: Authentication failed for 'https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git/'
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 30, done.
Counting objects:   3% (1/30)
Counting objects:   6% (2/30)
Counting objects:  10% (3/30)
Counting objects:  13% (4/30)
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Counting objects:  30% (9/30)
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Counting objects:  36% (11/30)
Counting objects:  40% (12/30)
Counting objects:  43% (13/30)
Counting objects:  46% (14/30)
Counting objects:  50% (15/30)
Counting objects:  53% (16/30)
Counting objects:  56% (17/30)
Counting objects:  60% (18/30)
Counting objects:  63% (19/30)
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Counting objects:  93% (28/30)
Counting objects:  96% (29/30)
Counting objects: 100% (30/30)
Counting objects: 100% (30/30), done.
Delta compression using up to 4 threads
Compressing objects:   6% (1/16)
Compressing objects:  12% (2/16)
Compressing objects:  18% (3/16)
Compressing objects:  25% (4/16)
Compressing objects:  31% (5/16)
Compressing objects:  37% (6/16)
Compressing objects:  43% (7/16)
Compressing objects:  50% (8/16)
Compressing objects:  56% (9/16)
Compressing objects:  62% (10/16)
Compressing objects:  68% (11/16)
Compressing objects:  75% (12/16)
Compressing objects:  81% (13/16)
Compressing objects:  87% (14/16)
Compressing objects:  93% (15/16)
Compressing objects: 100% (16/16)
Compressing objects: 100% (16/16), done.
Writing objects:   6% (1/16)
Writing objects:  12% (2/16)
Writing objects:  18% (3/16)
Writing objects:  25% (4/16)
Writing objects:  31% (5/16)
Writing objects:  37% (6/16)
Writing objects:  43% (7/16)
Writing objects:  50% (8/16)
Writing objects:  56% (9/16)
Writing objects:  62% (10/16)
Writing objects:  68% (11/16)
Writing objects:  75% (12/16)
Writing objects:  81% (13/16)
Writing objects:  87% (14/16)
Writing objects:  93% (15/16)
Writing objects: 100% (16/16)
Writing objects: 100% (16/16), 71.97 KiB | 402.00 KiB/s, done.
Total 16 (delta 13), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   eda1cca..64fe2ee  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B1[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [2], line 1
----> 1 B1[Integer(0)]

NameError: name 'B1' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[0]

[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^18 + 4*x^16 + 4*x^14 + x^8 + x^6 + x^4)/(x^4 + 2*x^2 + 1))*y]), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y), [(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^2 + 1)/(x^4 + 2*x^2 + 1))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0][?7h[?12l[?25h[?25l[?7l[].omega0[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h[3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.r()

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.r()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lla[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.r().regular_form()

[?7h[?12l[?25h[?2004l[?7h(3*x*y) dx + (3*x^2 + 2) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lsage: f1 = f(x = x^5 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(f1, m, prec = 500)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((x/y) dx, 0, (x/y) dx),
 ((x^2/y) dx, 0, (x^2/y) dx),
 ((x^3/y) dx, 0, (x^3/y) dx),
 ((x^4/y) dx, 0, (x^4/y) dx),
 ((x^5/y) dx, 0, (x^5/y) dx),
 ((x^6/y) dx, 0, (x^6/y) dx),
 (((-2*x^13 - 2*x^9 - 2*x^3 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx),
 (((x^12 - x^8 - x^4 + x^2 + 1)/y) dx, 2/x^2*y, (2/(x^2*y)) dx),
 (((-x^11 - 2*x^3 - x)/y) dx, 2/x^3*y, (2/(x*y)) dx),
 (((2*x^10 + x^6 + 2*x^2 + 2)/y) dx, 2/x^4*y, ((-2)/(x^4*y)) dx),
 (((2*x^5 + x)/y) dx, 2/x^5*y, ((-2*x^2 + 1)/(x^5*y)) dx),
 (((-2*x^8 - 2*x^4)/y) dx, 2/x^6*y, ((2*x^4 + x^2 - 1)/(x^6*y)) dx),
 (((x^7 - x^3)/y) dx, 2/x^7*y, ((x^6 - x^4 - x^2 + 2)/(x^7*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7lx^36 +2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4).factor()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: (x^5 - x)^4

[?7h[?12l[?25h[?2004l[?7hx^20 + x^16 + x^12 + x^8 + x^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A.h2.function)[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[4]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In [14], line 1
----> 1 C.de_rham_basis()[Integer(4)]

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[0]

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis()[4]

[?7h[?12l[?25h[?2004l[?7h((x^4/y) dx, 0, (x^4/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[4][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis()[4].omega0.regular_form()

[?7h[?12l[?25h[?2004l[?7h((3*x^9 + 2*x^5)*y) dx + (2*x^14 + x^10 + 2*x^6 + 3*x^4) dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7ldic_expansion(x^7, x^3 - x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: adic_expansion

 adic_expansion           

 adic_expansion_polynomial





 [?7h[?12l[?25h[?25l[?7l(x^7, x^3 - x)[?7h[?12l[?25h[?25l[?7l

 adic_expansion           



 <unknown> [?7h[?12l[?25h[?25l[?7l_polynomial

 adic_expansion           

 adic_expansion_polynomial[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l3*x^9 + 2*x^5[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(3*x^9 + 2*x^5, x^5 - x)

[?7h[?12l[?25h[?2004l[?7h3*x^4*t
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(3*x^9 + 2*x^5, x^5 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(3*x^9 + 2*x^5, x^5 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 -x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l2*14 + x^10 + 2*x^6 + 3*x^4, x^5 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^14 + x^10 + 2*x^6 + 3*x^4, x^5 - x)

[?7h[?12l[?25h[?2004l[?7h2*x^4*t^2 + 3*x^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^14 + x^10 + 2*x^6 + 3*x^4, x^5 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lic_expansion_polynomial(2*x^14 + x^10 + 2*x^6 + 3*x^4, x^5 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l,x^5 -x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7lx^119+4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
3

....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +

....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(



)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
3

....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +

....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)

[?7h[?12l[?25h[?2004l[?7h(x^4 + 2)*t^23 + 2*x*t^22 + 3*t^21 + (3*x^3 + 4*x)*t^20 + (2*x^4 + x^2 + 3)*t^19 + (2*x^3 + x)*t^18 + (3*x^4 + 4*x^2)*t^17 + (4*x^3 + x)*t^16 + (4*x^4 + 4*x^2 + 1)*t^15 + (4*x^3 + 4*x)*t^14 + (4*x^4 + 3*x^2 + 4)*t^13 + (3*x^3 + 4*x)*t^12 + (3*x^4 + 1)*t^11 + 3*x*t^10 + (2*x^4 + 4*x^2 + 2)*t^9 + (x^3 + 4*x)*t^8 + (4*x^4 + x^2 + 2)*t^7 + (3*x^3 + x)*t^6 + (4*x^4 + x^2)*t^5 + 4*x^3*t^4 + (x^4 + 4*x^2)*t^3 + t
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ( ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmulle
r

....: ().diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89

....: + 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x
^

....: 47 + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19

....: + 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^1
1

....: 4 + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 +

....: C1.x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 
+

....:  3*C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 
2

....: *C1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l....: *C1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()

....: [?7h[?12l[?25h[?25l[?7l....: 

....: [?7h[?12l[?25h[?25l[?7l....: 

....: [?7h[?12l[?25h[?25l[?7l

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lom = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114

....: + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C
1

....: .x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 
3

....: *C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*
C

....: 1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114

....: + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C
1

....: .x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 
3

....: *C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*
C

....: 1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [21], line 1
----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one).teichmuller()*C1.y.diffn()).verschiebung()

File <string>:81, in __add__(self, other)

AttributeError: 'NoneType' object has no attribute 'h1'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
 

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
 

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114
 

....: + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C
1

....: .x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 
3

....: *C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*
C

....: 1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn()

[?7h[?12l[?25h[?2004l
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lom = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form())

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [25], line 1
----> 1 xi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form())

NameError: name 'xi' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, f); xi = xi.reduce(); print(xi.regular_form()[?7h[?12l[?25h[?25l[?7l, f); xi = xi.reduce(); print(xi.regular_form()[?7h[?12l[?25h[?25l[?7lo, f); xi = xi.reduce(); print(xi.regular_form()[?7h[?12l[?25h[?25l[?7lm, f); xi = xi.reduce(); print(xi.regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form())

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [26], line 1
----> 1 xi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form())

File <string>:6, in __init__(self, omega0, f)

File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'diffn'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [27], line 1
----> 1 xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())

File <string>:92, in regular_drw_cech(cocycle)

File <string>:84, in regular_drw_form(omega)

File <string>:9, in decomposition_g0_pth_power(fct)

AttributeError: 'NoneType' object has no attribute 'int'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi

[?7h[?12l[?25h[?2004l[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7limport itertools[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.r()

[?7h[?12l[?25h[?2004l[?7h((x^4/y) dx, 0, (x^4/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.r()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.regular_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [30], line 1
----> 1 xi.regular_form()

File <string>:92, in regular_drw_cech(cocycle)

File <string>:84, in regular_drw_form(omega)

File <string>:9, in decomposition_g0_pth_power(fct)

AttributeError: 'NoneType' object has no attribute 'int'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct):

....:     print(fct)

....:     C = fct.curve

....:     Fxy, Rxy, xy, y = C.fct_field

....:     if fct.function in Rxy:

....:         return (fct, 0*C.x)

....:     '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).'''

....:     omega = fct.diffn().regular_form()

....:     print(omega)

....:     g0 = omega.int()

....:     A = (fct - g0).pth_root()

....:     return (g0, A)[?7h[?12l[?25h[?25l[?7l....:     return (g0, A)

....: [?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct):

....:     print(fct)

....:     C = fct.curve

....:     Fxy, Rxy, xy, y = C.fct_field

....:     if fct.function in Rxy:

....:         return (fct, 0*C.x)

....:     '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).'''

....:     omega = fct.diffn().regular_form()

....:     print(omega)

....:     g0 = omega.int()

....:     A = (fct - g0).pth_root()

....:     return (g0, A)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct):

....:     print(fct)

....:     C = fct.curve

....:     Fxy, Rxy, xy, y = C.fct_field

....:     if fct.function in Rxy:

....:         return (fct, 0*C.x)

....:     '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).'''

....:     omega = fct.diffn().regular_form()

....:     print(omega)

....:     g0 = omega.int()

....:     A = (fct - g0).pth_root()

....:     return (g0, A)[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lxi.regular_form()

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lsage: xi.regular_form()

[?7h[?12l[?25h[?2004l((3*x^98 + x^94 + 4*x^92 + 2*x^90 + x^86 + 3*x^84 + x^82 + 3*x^78 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + 4*x^68 + 2*x^66 + 3*x^64 + 2*x^62 + 4*x^60 + x^56 + 2*x^54 + 4*x^52 + 3*x^50 + 4*x^48 + 2*x^46 + 3*x^44 + x^38 + 4*x^36 + 3*x^34 + x^32 + 4*x^30 + 4*x^28 + x^26 + 3*x^24 + x^22 + 2*x^18 + 2*x^14 + x^12 + 2*x^10 + 2*x^6 + 3*x^4 + 2*x^2 + 2)/x^2)*y
None
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [32], line 1
----> 1 xi.regular_form()

File <string>:92, in regular_drw_cech(cocycle)

File <string>:84, in regular_drw_form(omega)

Cell In [31], line 10, in decomposition_g0_pth_power(fct)
      8 omega = fct.diffn().regular_form()
      9 print(omega)
---> 10 g0 = omega.int()
     11 A = (fct - g0).pth_root()
     12 return (g0, A)

AttributeError: 'NoneType' object has no attribute 'int'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
^C---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
File /ext/sage/9.8/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category()
    838 try:
--> 839     return self.__cached_methods[name]
    840 except KeyError:

KeyError: '_mpoly_base_ring'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring.py:1117, in PolynomialRing_general._mpoly_base_ring(self, variables)
   1116 try:
-> 1117     return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
   1118 except AttributeError:

File /ext/sage/9.8/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
    832 """
--> 833 return self.getattr_from_category(name)
    834 

File /ext/sage/9.8/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
    847 
--> 848             attr = getattr_from_other_class(self, cls, name)
    849             self.__cached_methods[name] = attr

File /ext/sage/9.8/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
    355     dummy_error_message.name = name
--> 356     raise AttributeError(dummy_error_message)
    357 cdef PyObject* attr = instance_getattr(cls, name)

AttributeError: 'FpT_with_category' object has no attribute '_mpoly_base_ring'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Cell In [33], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:11

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:24, in de_rham_witt_lift(cech_class, prec)

File <string>:6, in de_rham_witt_lift_form0(omega)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__()
   2404         return x
   2405 
-> 2406     return coercion_model.bin_op(left, right, operator.mul)
   2407 
   2408 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:82, in __pow__(self, exp)

File <string>:14, in __init__(self, C, g)

File <string>:263, in reduction(C, g)

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    894 if mor is not None:
    895     if no_extra_args:
--> 896         return mor._call_(x)
    897     else:
    898         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:920, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    918 
    919         elif isinstance(element, polynomial_element.Polynomial):
--> 920             if base_ring.has_coerce_map_from(element.parent()._mpoly_base_ring(self.variable_names())):
    921                 return self(element._mpoly_dict_recursive(self.variable_names(), base_ring))
    922 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring.py:1119, in PolynomialRing_general._mpoly_base_ring(self, variables)
   1117     return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
   1118 except AttributeError:
-> 1119     return self.base_ring()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.regular_form([?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct):

....:     print(fct)

....:     C = fct.curve

....:     Fxy, Rxy, xy, y = C.fct_field

....:     if fct.function in Rxy:

....:         return (fct, 0*C.x)

....:     '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).'''

....:     omega = fct.diffn().regular_form()

....:     print(omega)

....:     g0 = omega.int()

....:     A = (fct - g0).pth_root()

....:     return (g0, A)[?7h[?12l[?25h[?25l[?7lxi.regular_form()

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())

[?7h[?12l[?25h[?2004l
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File <string>:261, in reduction(C, g)

File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
   1514 if BOTH_ARE_ELEMENT(cl):
-> 1515     return coercion_model.bin_op(left, right, mul)
   1516 

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1310 if x_map is not None:
-> 1311     x_elt = (<Map>x_map)._call_(x)
   1312 else:

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:

File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
    197 if var in self._parent.variable_names():
--> 198     return R(self.polynomial(self._parent(var)))
    199 return R([self])

File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
    409 # Make polynomial ring over all variables except var.
--> 410 S = R.base_ring()[tuple(Z)]
    411 ring = S[var]

File /ext/sage/9.8/src/sage/structure/parent.pyx:1274, in sage.structure.parent.Parent.__getitem__()
   1273         return self.list()[n]
-> 1274 return meth(n)
   1275 

File /ext/sage/9.8/src/sage/categories/rings.py:1220, in Rings.ParentMethods.__getitem__(self, arg)
   1219 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1220 return PolynomialRing(self, elts)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:678, in PolynomialRing(base_ring, *args, **kwds)
    676         raise TypeError("you must specify the names of the variables")
--> 678 names = normalize_names(n, names)
    680 # At this point, we have only handled the "names" keyword if it was
    681 # needed. Since we know the variable names, it would logically be
    682 # an error to specify an additional "names" keyword. However,
   (...)
    685 # and we allow this for historical reasons. However, the names
    686 # must be consistent!

File /ext/sage/9.8/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
    899 
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
    901     r"""

File /ext/sage/9.8/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
    992     # Convert names to strings and strip whitespace
--> 993     names = [str(x).strip() for x in names]
    994 else:

File /ext/sage/9.8/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
    193     return super().__repr__()
--> 194 result = reprfunc()
    195 if isinstance(result, str):

File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2464, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular._repr_()
   2463 cdef ring *_ring = self._parent_ring
-> 2464 s = singular_polynomial_str(self._poly, _ring)
   2465 return s

File /ext/sage/9.8/src/sage/libs/singular/polynomial.pyx:440, in sage.libs.singular.polynomial.singular_polynomial_str()
    439 s = bytes_to_str(p_String(p, r, r))
--> 440 s = plusminus_pattern.sub("\\1 \\2 ", s)
    441 s = parenthvar_pattern.sub("\\1", s)

File /ext/sage/9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/re/__init__.py:315, in _subx(pattern, template)
    313     return _parser.expand_template(template, match)
--> 315 def _subx(pattern, template):
    316     # internal: Pattern.sub/subn implementation helper
    317     template = _compile_repl(template, pattern)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Cell In [34], line 1
----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y) *C1.x.diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one)*C1.y.diffn()).verschiebung()
      3 ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()
      5 xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

    [... skipping similar frames: __rmul__ at line 55 (9 times), sage.rings.integer.Integer.__mul__ at line 1961 (8 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (8 times)]

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:31, in __add__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [35], line 1
----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y) *C1.x.diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one)*C1.y.diffn()).verschiebung()
      3 ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()
      5 xi = superelliptic_drw_cech(om, ff)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__()
   2404         return x
   2405 
-> 2406     return coercion_model.bin_op(left, right, operator.mul)
   2407 
   2408 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

    [... skipping similar frames: __rmul__ at line 43 (10 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (10 times), sage.structure.element.Element.__mul__ at line 1527 (10 times)]

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:82, in __pow__(self, exp)

File <string>:14, in __init__(self, C, g)

File <string>:253, in reduction(C, g)

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    894 if mor is not None:
    895     if no_extra_args:
--> 896         return mor._call_(x)
    897     else:
    898         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.8/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
    704 x0, y0 = x, y
    705 try:
--> 706     x, y = resolve_fractions(x0, y0)
    707 except (AttributeError, TypeError):
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))

File /ext/sage/9.8/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
    682 def resolve_fractions(x, y):
--> 683     xn = x.numerator()
    684     xd = x.denominator()
    685     yn = y.numerator()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[4].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
 

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l1fx = x^5 - x)

 

 

 [?7h[?12l[?25h[?25l[?7l = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lsage: f1 = f(x = x^5 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[4].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[4].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(f1, m, prec = 500)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lff(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lom((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.regla_form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.reduce()

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File <string>:58, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Cell In [39], line 1
----> 1 xi.reduce()

File <string>:18, in reduce(self)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

    [... skipping similar frames: __rmul__ at line 55 (4 times), sage.rings.integer.Integer.__mul__ at line 1961 (3 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times)]

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:7, in __init__(self, C, g)

File <string>:282, in reduction_form(C, g)

File <string>:260, in reduction(C, g)

File /ext/sage/9.8/src/sage/arith/misc.py:2021, in xgcd(a, b)
   1933 r"""
   1934 Return a triple ``(g,s,t)`` such that `g = s\cdot a+t\cdot b = \gcd(a,b)`.
   1935 
   (...)
   2018     (1, 7*a^2/b^2, (((-h)*a)/b^2)*y + 1/b)
   2019 """
   2020 try:
-> 2021     return a.xgcd(b)
   2022 except AttributeError:
   2023     a = py_scalar_to_element(a)

File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
   4495 def new_method(self, other, *args, **kwargs):
   4496     if have_same_parent(self, other):
-> 4497         return method(self, other, *args, **kwargs)
   4498     else:
   4499         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:8931, in sage.rings.polynomial.polynomial_element.Polynomial.xgcd()
   8929 """
   8930 if hasattr(self.base_ring(), '_xgcd_univariate_polynomial'):
-> 8931     return self.base_ring()._xgcd_univariate_polynomial(self, other)
   8932 else:
   8933     raise NotImplementedError("%s does not provide an xgcd implementation for univariate polynomials"%self.base_ring())

File /ext/sage/9.8/src/sage/categories/fields.py:285, in Fields.ParentMethods._xgcd_univariate_polynomial(self, a, b)
    282         a = a.monic()
    283     return a
--> 285 def _xgcd_univariate_polynomial(self, a, b):
    286     r"""
    287     Return an extended gcd of ``a`` and ``b``.
    288 
   (...)
    359         (0, 0, 0)
    360     """
    361     R = a.parent()

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def reducee(self):

....: ^IC = self.curve

....: ^Ifct = self.f

....: ^If_first_comp = fct.t

....: ^If_second_comp = fct.f

....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp)

....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp)

....: ^Inew = self

....: ^Iprint(decomp_first_comp, decomp_second_comp)

....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()

....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()

....: ^Iprint(new.omega0)

....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()

....: ^Inew.omega8 = new.omega0 - new.f.diffn()

....: ^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^Ireturn new

....: [?7h[?12l[?25h[?25l[?7lsage: def reducee(self):

....: ^IC = self.curve

....: ^Ifct = self.f

....: ^If_first_comp = fct.t

....: ^If_second_comp = fct.f

....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp)

....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp)

....: ^Inew = self

....: ^Iprint(decomp_first_comp, decomp_second_comp)

....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()

....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()

....: ^Iprint(new.omega0)

....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()

....: ^Inew.omega8 = new.omega0 - new.f.diffn()

....: ^Ireturn new

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(B[0].omega0)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: reducee(xi)

[?7h[?12l[?25h[?2004l(0, 0, 0) (((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y, 0, 1/x^2*y)
[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])
[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def reducee(self):

....: ^IC = self.curve

....: ^Ifct = self.f

....: ^If_first_comp = fct.t

....: ^If_second_comp = fct.f

....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp)

....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp)

....: ^Inew = self

....: ^Iprint('decomp_first_comp[0], decomp_second_comp[0]', decomp_first_comp[0], decomp_second_comp[0])

....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()

....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()

....: ^Iprint('new.omega0', new.omega0)

....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()

....: ^Inew.omega8 = new.omega0 - new.f.diffn()

....: ^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^Ireturn new

....: [?7h[?12l[?25h[?25l[?7lsage: def reducee(self):

....: ^IC = self.curve

....: ^Ifct = self.f

....: ^If_first_comp = fct.t

....: ^If_second_comp = fct.f

....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp)

....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp)

....: ^Inew = self

....: ^Iprint('decomp_first_comp[0], decomp_second_comp[0]', decomp_first_comp[0], decomp_second_comp[0])

....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()

....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()

....: ^Iprint('new.omega0', new.omega0)

....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()

....: ^Inew.omega8 = new.omega0 - new.f.diffn()

....: ^Ireturn new

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lucee(xi)[?7h[?12l[?25h[?25l[?7lsage: reducee(xi)

[?7h[?12l[?25h[?2004ldecomp_first_comp[0], decomp_second_comp[0] 0 2/x^2*y
new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f[?7h[?12l[?25h[?25l[?7lsage: xi.f



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.coordinates(prec = 500)[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates(prec = 500)



 [?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: xi.f.t

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef reducee(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition

 decomposition               decomposition_g0_pth_power  decomposition_omega0_hpdh  

 decomposition_g0_g8         decomposition_g8_p2th_power decomposition_omega0_omega8

 decomposition_g0_p2th_power decomposition_g8_pth_power  decomposition_omega8_hpdh  



 [?7h[?12l[?25h[?25l[?7l_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7l

 decomposition              





 <unknown> [?7h[?12l[?25h[?25l[?7l_g0_pth_power

 decomposition               decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7l82th_power

 decomposition_g0_pth_power 

 decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l0g8



 decomposition_g0_g8         decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l(xi.f)







[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f.t)

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lxi.f.t[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f.t)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f.t)

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lxi.f.t[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: xi.f

[?7h[?12l[?25h[?2004l[?7hV(4/x^2*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def aa(self):

....:     new = self

....: ^Inew += 1

....: ^Ireturn new[?7h[?12l[?25h[?25l[?7lsage: def aa(self):

....:     new = self

....: ^Inew += 1

....: ^Ireturn new

[?7h[?12l[?25h[?2004l  Cell In [48], line 3
    new += Integer(1)
    ^
TabError: inconsistent use of tabs and spaces in indentation

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def aa(self):

....: ^Inew = self

....: ^Inew += 1

....: ^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^Ireturn new

....: [?7h[?12l[?25h[?25l[?7lsage: def aa(self):

....: ^Inew = self

....: ^Inew += 1

....: ^Ireturn new

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef aa(self):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: d = 1

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
3

....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +
 

....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7la

 

 [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aa(d)

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld = 1[?7h[?12l[?25h[?25l[?7lsage: d

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

....: 

....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

....: 

....: xi = superelliptic_drw_cech(om, ff)

[?7h[?12l[?25h[?2004l
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lucee(xi)[?7h[?12l[?25h[?25l[?7lsage: reducee(xi)

[?7h[?12l[?25h[?2004ldecomp_first_comp[0], decomp_second_comp[0] 0 ((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y
new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])
[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7lsage: reducee(xi)

[?7h[?12l[?25h[?2004ldecomp_first_comp[0], decomp_second_comp[0] 0 2/x^2*y
new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lef aa(self):[?7h[?12l[?25h[?25l[?7lcompoition_g0_g8(xi.f.t)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(xi.f.t)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [56], line 1
----> 1 decomposition_g0_g8(ff)

File <string>:7, in decomposition_g0_g8(fct, prec)

AttributeError: 'superelliptic_witt' object has no attribute 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f)

[?7h[?12l[?25h[?2004l[?7h(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y,
 0,
 1/x^2*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f)[0]

[?7h[?12l[?25h[?2004l[?7h((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF = GF(p)[?7h[?12l[?25h[?25l[?7lxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C1.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f)[0] in Rxy

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[4].oega0.regular_form()[?7h[?12l[?25h[?25l[?7ly.diffn()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C1.y/C1.x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lrt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C1.y/C1.x^2).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-11 + 3*t^29 + 4*t^89 + t^109 + 2*t^129 + 2*t^149 + 4*t^169 + t^229 + 2*t^269 + t^289 + 2*t^309 + 3*t^329 + t^369 + 2*t^389 + 3*t^449 + t^469 + O(t^489)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
 

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()

 

 

 [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 3, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lff.f.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
 

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l-

 

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l

  C1.a_number                               C1.cartier_matrix                         C1.de_rham_basis                           

  C1.base_ring                              C1.characteristic                         C1.degrees_de_rham0                        

                  C1.basis_de_rham_degrees                  C1.cohomology_of_structure_sheaf_basis    C1.degrees_de_rham1                       >

  C1.basis_holomorphic_differentials_degree C1.crystalline_cohomology_basis           C1.degrees_holomorphic_differentials       

 [?7h[?12l[?25h[?25l[?7la_number

 C1.a_number                              







 <unknown> [?7h[?12l[?25h[?25l[?7lcartier_matrix

 C1.a_number                               C1.cartier_matrix                        [?7h[?12l[?25h[?25l[?7lde_rhambsis

 C1.cartier_matrix                         C1.de_rham_basis                         [?7h[?12l[?25h[?25l[?7lcartiermtrix

 C1.cartier_matrix                         C1.de_rham_basis                         [?7h[?12l[?25h[?25l[?7lharacteristc

 C1.cartier_matrix                        

 C1.characteristic                        [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis



 C1.characteristic                        

 C1.cohomology_of_structure_sheaf_basis   [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: ff - 3*C1.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [63], line 1
----> 1 ff - Integer(3)*C1.cohomology_of_structure_sheaf_basis()[Integer(1)]

File <string>:35, in __sub__(self, other)

File <string>:29, in __add__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 't'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laf - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7laf - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lf - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aa = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[0] in Rxy[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(ff.f)[0] in Rxy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aa)

[?7h[?12l[?25h[?2004l[?7h(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 1)/x^2)*y,
 0,
 2/x^2*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aa)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_g0_g8(aa)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l)[0] in Rxy[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f)

[?7h[?12l[?25h[?2004l[?7h(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y,
 0,
 1/x^2*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.f.coordinates()[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lsage: ff.f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 3, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llogy_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: 3*C1.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l[?7h1/x^2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.f.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lsage: ff.f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 3, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aa.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l+ 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aa = ff.f + 3*C1.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = ff.f + 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: aa.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa.coordinates()[?7h[?12l[?25h[?25l[?7l = ff.f + 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l3*C1homology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.f.coordinates()[?7h[?12l[?25h[?25l[?7lor b in B1:[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for b in C1.cohomology_of_structure_sheaf_basis():

....: [?7h[?12l[?25h[?25l[?7lprint(omega)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb.regular_form())[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(b.coordinates())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C1.cohomology_of_structure_sheaf_basis():

....:     print(b.coordinates())

....: 

[?7h[?12l[?25h[?2004l[4, 0, 0, 0, 0, 0, 0]
[0, 4, 0, 0, 0, 0, 0]
[0, 0, 4, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0]
[0, 0, 0, 0, 4, 0, 0]
[0, 0, 0, 0, 0, 4, 0]
[0, 0, 0, 0, 0, 0, 4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor b in C1.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l1 = f(x= x^5 - x)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lsage: f1 = f(x = x^5 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(f1, m, prec = 500)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lf.f.coordinates()[?7h[?12l[?25h[?25l[?7l - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
 

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

*C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34


+ 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_g0_g8(ff.f)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f)

[?7h[?12l[?25h[?2004l[?7h((2*x^96 + 4*x^92 + x^90 + 3*x^88 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^76 + x^74 + 3*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + 2*x^62 + 3*x^60 + x^58 + 4*x^54 + 3*x^52 + x^50 + 2*x^48 + x^46 + 3*x^44 + 2*x^42 + 4*x^36 + x^34 + 2*x^32 + 4*x^30 + x^28 + x^26 + 4*x^24 + 2*x^22 + 4*x^20 + 3*x^16 + 3*x^12 + 4*x^10 + 3*x^8 + 3*x^4 + 2*x^2 + 3)*y,
 0,
 4/x^2*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
 

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
 

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
 

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
 

....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

.diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +


2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

 + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +


2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +


3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2


+ C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om, ff)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce()

[?7h[?12l[?25h[?2004l(0, 0, 0) ((2*x^96 + 4*x^92 + x^90 + 3*x^88 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^76 + x^74 + 3*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + 2*x^62 + 3*x^60 + x^58 + 4*x^54 + 3*x^52 + x^50 + 2*x^48 + x^46 + 3*x^44 + 2*x^42 + 4*x^36 + x^34 + 2*x^32 + 4*x^30 + x^28 + x^26 + 4*x^24 + 2*x^22 + 4*x^20 + 3*x^16 + 3*x^12 + 4*x^10 + 3*x^8 + 3*x^4 + 2*x^2 + 3)*y, 0, 4/x^2*y)
[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce()

[?7h[?12l[?25h[?2004l(0, 0, 0) (0, 0, 4/x^2*y)
[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce()

[?7h[?12l[?25h[?2004l(0, 0, 0) (0, 0, 4/x^2*y)
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [83], line 1
----> 1 xi.reduce()

File <string>:20, in reduce(self)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__()
   2404         return x
   2405 
-> 2406     return coercion_model.bin_op(left, right, operator.mul)
   2407 
   2408 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:48, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

    [... skipping similar frames: __rmul__ at line 43 (6 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (6 times), sage.structure.element.Element.__mul__ at line 1527 (6 times)]

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:43, in __rmul__(self, other)

File <string>:31, in __add__(self, other)

File <string>:82, in __pow__(self, exp)

File <string>:14, in __init__(self, C, g)

File <string>:253, in reduction(C, g)

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    894 if mor is not None:
    895     if no_extra_args:
--> 896         return mor._call_(x)
    897     else:
    898         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.8/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
    709                     x0, y0, self))
    710 try:
--> 711     return self._element_class(self, x, y, coerce=coerce)
    712 except TypeError:
    713     if parent(x) is parent(x0):

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: class test:

....: ^Idef __init__(self, gg):

....: ^I^Iself.gg = gg

....: ^I

....: ^Idef aa(self):

....: ^I^Inew = self.gg

....: ^I^Inew += 1

....: ^I^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn new

....: [?7h[?12l[?25h[?25l[?7lsage: class test:

....: ^Idef __init__(self, gg):

....: ^I^Iself.gg = gg

....: ^I

....: ^Idef aa(self):

....: ^I^Inew = self.gg

....: ^I^Inew += 1

....: ^I^Ireturn new

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D = test(1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD = test(1)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.aa()

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.aa()[?7h[?12l[?25h[?25l[?7lsage: D

[?7h[?12l[?25h[?2004l[?7h<__main__.test object at 0x7f22ef213390>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.aa()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: D.gg

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
 

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
 

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
 

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
 

....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

.diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +


2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

 + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +


2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +


3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2


+ C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C2 = superelliptic(x^7 + x + 1, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
 

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lor b in C1.cohomology_of_structure_sheaf_basis():

 

 

 [?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC1.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l2.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lprint(b.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(b.coordinates())[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C2.cohomology_of_structure_sheaf_basis():

....:     print(b.coordinates())

....: 

[?7h[?12l[?25h[?2004l[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C2.cohomology_of_structure_sheaf_basis():

....:     print(b.coordinates())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lbasis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lbasis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lbasis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7ld_basis():[?7h[?12l[?25h[?25l[?7le_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lr_basis():[?7h[?12l[?25h[?25l[?7lh_basis():[?7h[?12l[?25h[?25l[?7la_basis():[?7h[?12l[?25h[?25l[?7lm_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(b.coordinates())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C2.de_rham_basis():

....:     print(b.coordinates())

....: 

[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0)
(0, 1, 0, 0, 0, 0)
(0, 0, 1, 0, 0, 0)
(0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 1, 0)
(0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C2.de_rham_basis():

....:     print(b.coordinates())[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l.:[?7h[?12l[?25h[?25l[?7lh:[?7h[?12l[?25h[?25l[?7lo:[?7h[?12l[?25h[?25l[?7lm:[?7h[?12l[?25h[?25l[?7lo:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

....: 

....:     print(b.coordinates())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l    print(b.coordinates())

 [?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C2.holomorphic_differentials_basis():

....:     print(b.coordinates())

....: 

[?7h[?12l[?25h[?2004l[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""n"a"p"r"a"w"i"o"n"e" "C"."c"o"h"o"m"o"l"o"g"y"_"o"f"_"s"t"r"_"s"h"_""."c"o"o"r"d"i"n"a"t"e"s"." "A"l"e" "d"r"w"_"c"e"c"h"."r"e"d"u"c"e" "n"a"d"a"l" "z"m"i"e"n"i"a" "a"r"g"u"m"e"n"t"
[master a5c2ce2] naprawione C.cohomology_of_str_sh.coordinates. Ale drw_cech.reduce nadal zmienia argument
 3 files changed, 1586 insertions(+), 6 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 15, done.
Counting objects:   6% (1/15)
Counting objects:  13% (2/15)
Counting objects:  20% (3/15)
Counting objects:  26% (4/15)
Counting objects:  33% (5/15)
Counting objects:  40% (6/15)
Counting objects:  46% (7/15)
Counting objects:  53% (8/15)
Counting objects:  60% (9/15)
Counting objects:  66% (10/15)
Counting objects:  73% (11/15)
Counting objects:  80% (12/15)
Counting objects:  86% (13/15)
Counting objects:  93% (14/15)
Counting objects: 100% (15/15)
Counting objects: 100% (15/15), done.
Delta compression using up to 8 threads
Compressing objects:  12% (1/8)
Compressing objects:  25% (2/8)
Compressing objects:  37% (3/8)
Compressing objects:  50% (4/8)
Compressing objects:  62% (5/8)
Compressing objects:  75% (6/8)
Compressing objects:  87% (7/8)
Compressing objects: 100% (8/8)
Compressing objects: 100% (8/8), done.
Writing objects:  12% (1/8)
Writing objects:  25% (2/8)
Writing objects:  37% (3/8)
Writing objects:  50% (4/8)
Writing objects:  62% (5/8)
Writing objects:  75% (6/8)
Writing objects:  87% (7/8)
Writing objects: 100% (8/8)
Writing objects: 100% (8/8), 19.86 KiB | 207.00 KiB/s, done.
Total 8 (delta 7), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   64fe2ee..a5c2ce2  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
 

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
 

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
 

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
 

....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

.diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +


2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

 + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +


2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +


3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2


+ C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2

....: + C1.one)*C1.y.diffn()).verschiebung()

[?7h[?12l[?25h[?2004lf[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lfor b in C2.holomorphic_differentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor b in C2.holomorphic_differentials_basis():[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
 

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

*C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34


+ 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(





)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(





)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(





)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(





)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(





)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(





)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()sd[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()sdffds

[?7h[?12l[?25h[?2004l  Cell In [3], line 1
    ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()sdffds
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
 

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()sdffds[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

*C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34


+ 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

ne)/C1.x^2)*C1.y).verschiebung()sdffds[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()sdffds

[?7h[?12l[?25h[?2004l  Cell In [4], line 1
    ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()sdffds
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()sdffds[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 
3

....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34

....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
o

....: ne)/C1.x^2)*C1.y).verschiebung()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = sprelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l= superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om, ff)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.redc()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce()

[?7h[?12l[?25h[?2004l[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce()

[?7h[?12l[?25h[?2004l[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: xi.omega0.h1

[?7h[?12l[?25h[?2004l[?7h(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.h1[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0.h1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.omega0.r()

[?7h[?12l[?25h[?2004l[?7h(x^4/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
( [0] d[x] + [2] d[y] + V((x^5 + 2*x^3 + 2*x^2 + 1) dy) + dV(0), V(((x^2 + x + 2)/x)*y) )
( [0] d[x] + [2*x] d[y] + V((x^8 + x^6 + x^5 + x^3 + x^2 + x + 1) dy) + dV(0), [2/x*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 1)/x)*y) )
( [0] d[x] + [1] d[y] + V((2*x + 1) dy) + dV(0), V((x + 2)*y) )
( [0] d[x] + [x] d[y] + V((x^12 + 2*x^11 + 2*x^4 + x^3) dy) + dV(0), V(((x^8 + 2*x^7 + 1)/x^4)*y) )
( [0] d[x] + [x^2] d[y] + V((2*x^15 + x^14 + 2*x^7 + x^6) dy) + dV(0), V(((x^10 + 2*x^9 + x^2 + x + 1)/x^3)*y) )
( [0] d[x] + [x^3] d[y] + V((2*x^10 + x^9 + 2*x^2 + x) dy) + dV(0), V((x^10 + 2*x^9 + x^2 + x + 1)*y) )
( [0] d[x] + [x^7] d[y] + V((x^30 + 2*x^29 + 2*x^22 + x^21 + x^14 + x^13 + 2*x^6 + x^4) dy) + dV(0), [2/x*y] + V(((x^26 + 2*x^25 + x^18 + x^17 + x^16 + x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^2 + 2*x + 1)/x^4)*y) )
( [0] d[x] + [2*x^6] d[y] + V((x^19 + 2*x^18 + x^10 + x^9 + 2*x^3 + x^2 + x + 2) dy) + dV(0), [2/x^2*y] + V((2*x^19 + x^18 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^3 + x^2 + 2*x + 1)*y) )
( [0] d[x] + [0] d[y] + V((x^8 + 1) dy) + dV(0), [2/x^3*y] )
( [0] d[x] + [x^4] d[y] + V((x^21 + 2*x^20 + 2*x^13 + x^12 + 2*x^5 + x^4) dy) + dV(0), [2/x^4*y] + V(((x^17 + 2*x^16 + x^9 + x^8 + x^7 + x + 2)/x^4)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa.coordinates()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
3

....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +
 

....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
3

....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +
 

....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt

 

 [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lion

 adic_expansion           

                     adic_expansion_polynomial





 [?7h[?12l[?25h[?25l[?7l_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
3

....:  + 4*x^81 + x^3 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +
 

....: 2*x^31 + 3*x^2 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7l

 adic_expansion           



 <unknown> [?7h[?12l[?25h[?25l[?7l_polynomial

                     adic_expansion           

                     adic_expansion_polynomial[?7h[?12l[?25h[?25l[?7l(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
3

....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +
 

....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)

[?7h[?12l[?25h[?25l[?7l2*x^15 + x^14 + 2*x^7 + x^6

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f)

[?7h[?12l[?25h[?2004l[?7h2*t^5 + (x^2 + 2*x + 1)*t^4 + (x^2 + 2*x + 1)*t^3 + (2*x^2 + 2*x + 1)*t^2 + x*t + x^2 + x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lfor N in range(1, 7):[?7h[?12l[?25h[?25l[?7lsage: f

[?7h[?12l[?25h[?2004l[?7hx^3 + x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lC2 = superelliptic(x^7 + x + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + 2*x + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1 = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(x^5 + 2*x^3 + 2*x^2 + 1)[?7h[?12l[?25h[?25l[?7lsage: f1 = (x^5 + 2*x^3 + 2*x^2 + 1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = (x^5 + 2*x^3 + 2*x^2 + 1)[?7h[?12l[?25h[?25l[?7l2.diffn().int()[?7h[?12l[?25h[?25l[?7l = 1.pth_root()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(2*x^15 + x^14 + 2*x^7 + x^6)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7lsage: f2 = -((2*x^15 + x^14 + 2*x^7 + x^6)

....: [?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7lsage: f2 = -((2*x^15 + x^14 + 2*x^7 + x^6)

....: )

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2 = -((2*x^15 + x^14 + 2*x^7 + x^6)[?7h[?12l[?25h[?25l[?7l1(x^5 + 2*x^3 + 2*x^ + 1)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf(x = x^5 - x)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1 = f1(x = x^3 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f1(x = x^3 - x)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1

[?7h[?12l[?25h[?2004l[?7hx^15 + x^13 + x^11 + x^9 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + x^3 + 2*x^2 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = f1(x = x^3 - x)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l2 = -((2*x^15 + x^14 + 2*x^7 + x^6)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f2 - x^2*f1

[?7h[?12l[?25h[?2004l[?7h2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: adic_expansion

 adic_expansion           

 adic_expansion_polynomial





 [?7h[?12l[?25h[?25l[?7l_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f)[?7h[?12l[?25h[?25l[?7l

 adic_expansion           



 <unknown> [?7h[?12l[?25h[?25l[?7l_polynomial

 adic_expansion           

 adic_expansion_polynomial[?7h[?12l[?25h[?25l[?7l(2*x^15 + x^14 + 2*x^7 + x^6, f)





[?7h[?12l[?25h[?25l[?7l2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, f)

[?7h[?12l[?25h[?2004l[?7h(2*x^2 + 2)*t^5 + (x^2 + 2*x)*t^4 + (2*x^2 + 2)*t^3 + (2*x + 2)*t + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, f)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, f)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h2*t^5 + (x^2 + x + 1)*t^4 + (2*x^2 + x + 2)*t^3 + (x^2 + 2*x)*t^2 + (x^2 + 2*x + 1)*t + 2*x^2 + x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, x^3 - x)[?7h[?12l[?25h[?25l[?7l72*x^14+ 2*x^13 + 2*11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, f)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(2*x^2 + 1)*t^5 + (2*x^2 + 2*x + 2)*t^4 + (2*x^2 + 2*x + 1)*t^3 + x*t^2 + (2*x^2 + x + 2)*t + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^5 + x^4 + x^3 + x, x^3 + x + 1)

[?7h[?12l[?25h[?2004l[?7h(x^2 + x)*t + x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [16], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:7

NameError: name 'a' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lComputing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
az^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [17], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:13

File <string>:44, in crystalline_cohomology_basis(self, prec, info)

File <string>:26, in de_rham_witt_lift(cech_class, prec)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:27, in __add__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:70, in __rmul__(self, constant)

File <string>:14, in __init__(self, C, g)

File <string>:248, in reduction(C, g)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:693, in PolynomialRing(base_ring, *args, **kwds)
    690         raise TypeError("variable names specified twice inconsistently: %r and %r" % (names, kwnames))
    692 if multivariate or len(names) != 1:
--> 693     return _multi_variate(base_ring, names, **kwds)
    694 else:
    695     return _single_variate(base_ring, names, **kwds)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:813, in _multi_variate(base_ring, names, sparse, order, implementation)
    811 # "implementation" must be last
    812 key = [base_ring, names, n, order, implementation]
--> 813 R = _get_from_cache(key)
    814 if R is not None:
    815     return R

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:715, in _get_from_cache(key)
    713 def _get_from_cache(key):
    714     key = tuple(key)
--> 715     return _cache.get(key)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/IPython/core/interactiveshell.py:3433 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Cell In [18], line 1
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.8/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:32

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.8/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:37
    #print(M^3)
               ^
IndentationError: expected an indented block after 'for' statement on line 32

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [19], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:25

File <string>:19, in de_rham_witt_lift(cech_class, prec)

AttributeError: 'list' object has no attribute 'curve'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l( [0] d[x] + [2*a + 1] d[y] + V((2*x^5 + a*x^3 + x^2 + 2*a) dy) + dV(0), V((((2*a + 2)*x^2 + 2*a*x + 2*a + 1)/x)*y) )
( [0] d[x] + [a + 2] d[y] + V((2*x^3 + (a + 1)*x + 2*a) dy) + dV(0), V(((x^6 + (2*a + 2)*x^4 + a*x^3 + 2*a + 1)/x^3)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C1.y/C1.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7la^(-1))expansion_at_infy(prec = 100)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/xx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 1/(2*a+1)

[?7h[?12l[?25h[?2004l[?7h2*a
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: b1.curve

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + (a + 2)*x^3 + 2*a*x + 1 over Finite Field in a of size 3^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[4].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[4].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
 ((x/y) dx, 0, (x/y) dx),
 ((x^2/y) dx, 0, (x^2/y) dx),
 ((x^3/y) dx, 0, (x^3/y) dx),
 (((x^7 + (a - 1)*x)/y) dx, 2/x*y, (((-a)*x - 1)/(x^2*y)) dx),
 (((-x^6 + (-a + 1))/y) dx, 2/x^2*y, (1/(x^3*y)) dx),
 (0 dx, 2/x^3*y, (a/(x^3*y)) dx),
 ((x^4/y) dx, 2/x^4*y, (((-a + 1)*x^3 + (-a)*x - 1)/(x^5*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l( [0] d[x] + [2*a + 1] d[y] + V((2*x^5 + a*x^3 + x^2 + 2*a) dy) + dV(0), V((((2*a + 2)*x^2 + 2*a*x + 2*a + 1)/x)*y) )
( [0] d[x] + [(a + 2)*x^2] d[y] + V(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy) + dV(0), V(((x^12 + (2*a + 2)*x^10 + a*x^9 + (2*a + 1)*x^6 + 2*a*x^4 + x^3 + (a + 2)*x^2 + (2*a + 2)*x + a + 2)/x^3)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^5 + x^4 + x^3 + x, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion_polynomial(x^5 + x^4 + x^3 + x, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l((2*a1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x)[?7h[?12l[?25h[?25l[?7l- x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy, x^3 - x)

[?7h[?12l[?25h[?2004l  Cell In [25], line 1
    adic_expansion_polynomial(((Integer(2)*a + Integer(1))*x**Integer(17) + a*x**Integer(15) + Integer(2)*x**Integer(14) + Integer(2)*x**Integer(9) + (a + Integer(1))*x**Integer(7) + Integer(2)*a*x**Integer(6) + a*x**Integer(5) + (Integer(2)*a + Integer(1))*x**Integer(3) + (a + Integer(1))*x**Integer(2) + Integer(1)) dy, x**Integer(3) - x)
                               ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)

[?7h[?12l[?25h[?2004l[?7h((2*a + 1)*x^2 + 2*a + 2)*t^5 + (2*x^2 + 2*a*x + 2)*t^4 + ((2*a + 2)*x^2 + 2*x + a + 2)*t^3 + (2*x^2 + (a + 1)*x + 2*a + 1)*t^2 + (2*a*x^2 + a*x + a + 2)*t + (a + 2)*x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [1], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

AttributeError: 'superelliptic_form' object has no attribute 'mult_by_p'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: C.dx.expansion_at_infty()

 C.dx.cartier               C.dx.expansion_at_infty    C.dx.is_regular_on_U0      C.dx.reduce2               C.dx.verschiebung         

 C.dx.coordinates           C.dx.form                  C.dx.is_regular_on_Uinfty  C.dx.regular_form                                    

 C.dx.curve                 C.dx.int                   C.dx.jth_component         C.dx.residue                                         

 C.dx.expansion             C.dx.inv_cartier           C.dx.reduce                C.dx.serre_duality_pairing                           

 [?7h[?12l[?25h[?25l[?7lm







[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.mult_by_p()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [2], line 1
----> 1 C.dx.mult_by_p()

AttributeError: 'superelliptic_form' object has no attribute 'mult_by_p'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
V((x^5/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
V((x^8/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
V((x^11/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
V(((x^23 + (-a)*x^5)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
V(((-x^20 + a*x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
0
V((x^14/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod.pyx:379, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    378 try:
--> 379     z = integer_ring.Z(value)
    380 except (TypeError, ValueError):

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    895 if no_extra_args:
--> 896     return mor._call_(x)
    897 else:

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
    286 cdef Map m
--> 287 cdef Element e = method(C)
    288 if e is None:

File /ext/sage/9.8/src/sage/rings/finite_rings/element_givaro.pyx:1405, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._integer_()
   1404     return Integer(a)
-> 1405 raise TypeError("not in prime subfield")
   1406 

TypeError: not in prime subfield

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/finite_rings/hom_prime_finite_field.pyx:43, in sage.rings.finite_rings.hom_prime_finite_field.SectionFiniteFieldHomomorphism_prime._call_()
     42 try:
---> 43     return self._codomain._element_constructor(x)
     44 except TypeError:

File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod_ring.py:1191, in IntegerModRing_generic._element_constructor_(self, x)
   1190 try:
-> 1191     return integer_mod.IntegerMod(self, x)
   1192 except (NotImplementedError, PariError):

File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod.pyx:200, in sage.rings.finite_rings.integer_mod.IntegerMod()
    199 t = modulus.element_class()
--> 200 return t(parent, value)
    201 

File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod.pyx:387, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    386 if isinstance(value, Element) and value.parent().is_exact():
--> 387     value = sage.rings.rational_field.QQ(value)
    388     z = value % self.__modulus.sageInteger

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    895 if no_extra_args:
--> 896     return mor._call_(x)
    897 else:

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.8/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    537 if x is not None:
--> 538     self.__set_value(x, base)
    539 

File /ext/sage/9.8/src/sage/rings/rational.pyx:683, in sage.rings.rational.Rational.__set_value()
    682 else:
--> 683     raise TypeError("unable to convert {!r} to a rational".format(x))
    684 

TypeError: unable to convert 2*a to a rational

During handling of the above exception, another exception occurred:

ValueError                                Traceback (most recent call last)
Cell In [4], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:82, in regular_drw_form(omega)

File <string>:27, in decomposition_omega0_hpdh(omega)

File <string>:70, in cartier(self)

File <string>:133, in polynomial_part(p, h)

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    894 if mor is not None:
    895     if no_extra_args:
--> 896         return mor._call_(x)
    897     else:
    898         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162 
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
    467 elif isinstance(x, sage.rings.power_series_ring_element.PowerSeries):
    468     x = x.truncate()
--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:124, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
    122         except AttributeError:
    123             pass
--> 124     Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
    125 
    126 cdef Polynomial_template _new(self):

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_template.pxi:170, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
    168 elif isinstance(x, Polynomial):
    169     k = (<Polynomial_template>self)._parent.base_ring()
--> 170     x = [k(w) for w in list(x)]
    171     Polynomial_template.__init__(self, parent, x, check=True, is_gen=False, construct=construct)
    172 elif isinstance(x, FractionFieldElement) and (x.parent().base() is parent or x.parent().base() == parent) and x.denominator() == 1:

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    894 if mor is not None:
    895     if no_extra_args:
--> 896         return mor._call_(x)
    897     else:
    898         return mor._call_with_args(x, args, kwds)

File /ext/sage/9.8/src/sage/rings/finite_rings/hom_prime_finite_field.pyx:45, in sage.rings.finite_rings.hom_prime_finite_field.SectionFiniteFieldHomomorphism_prime._call_()
     43     return self._codomain._element_constructor(x)
     44 except TypeError:
---> 45     raise ValueError("%s is not in the image of %s" % (x, self._inverse))
     46 
     47 

ValueError: 2*a is not in the image of (map internal to coercion system -- copy before use)
Ring morphism:
  From: Finite Field of size 3
  To:   Finite Field in a of size 3^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7larent(A.h2.function)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field in a of size 3^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbparent(x)[?7h[?12l[?25h[?25l[?7laparent(x)[?7h[?12l[?25h[?25l[?7lsparent(x)[?7h[?12l[?25h[?25l[?7leparent(x)[?7h[?12l[?25h[?25l[?7l_parent(x)[?7h[?12l[?25h[?25l[?7lrparent(x)[?7h[?12l[?25h[?25l[?7liparent(x)[?7h[?12l[?25h[?25l[?7lnparent(x)[?7h[?12l[?25h[?25l[?7lgparent(x)[?7h[?12l[?25h[?25l[?7l(parent(x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: base_ring(parent(x))

[?7h[?12l[?25h[?2004l[?7hFinite Field in a of size 3^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
UnboundLocalError                         Traceback (most recent call last)
Cell In [7], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:82, in regular_drw_form(omega)

File <string>:27, in decomposition_omega0_hpdh(omega)

File <string>:70, in cartier(self)

File <string>:131, in polynomial_part(p, h)

UnboundLocalError: cannot access local variable 'x' where it is not associated with a value
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [8], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:84, in regular_drw_form(omega)

File <string>:10, in decomposition_g0_pth_power(fct)

File <string>:150, in pth_root(self)

File <string>:70, in cartier(self)

File <string>:138, in polynomial_part(p, h)

File /ext/sage/9.8/src/sage/rings/integer.pyx:655, in sage.rings.integer.Integer.__init__()
    653 otmp = getattr(x, "_integer_", None)
    654 if otmp is not None:
--> 655     set_from_Integer(self, otmp(the_integer_ring))
    656     return
    657 

File /ext/sage/9.8/src/sage/rings/finite_rings/element_givaro.pyx:1405, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._integer_()
   1403     if a < self._cache.objectptr.characteristic():
   1404         return Integer(a)
-> 1405     raise TypeError("not in prime subfield")
   1406 
   1407 def _log_to_int(FiniteField_givaroElement self):

TypeError: not in prime subfield
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lFinite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [9], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:84, in regular_drw_form(omega)

File <string>:10, in decomposition_g0_pth_power(fct)

File <string>:150, in pth_root(self)

File <string>:70, in cartier(self)

File <string>:139, in polynomial_part(p, h)

File /ext/sage/9.8/src/sage/rings/integer.pyx:655, in sage.rings.integer.Integer.__init__()
    653 otmp = getattr(x, "_integer_", None)
    654 if otmp is not None:
--> 655     set_from_Integer(self, otmp(the_integer_ring))
    656     return
    657 

File /ext/sage/9.8/src/sage/rings/finite_rings/element_givaro.pyx:1405, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._integer_()
   1403     if a < self._cache.objectptr.characteristic():
   1404         return Integer(a)
-> 1405     raise TypeError("not in prime subfield")
   1406 
   1407 def _log_to_int(FiniteField_givaroElement self):

TypeError: not in prime subfield
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lFinite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
Finite Field in a of size 3^2
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [10], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:85, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [11], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:85, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0
1
0
0
0
1
0
0
0
x^27 + (a + 2)*x^19 + x^13 + (a + 1)*x^11 + (2*a + 1)*x^10 + (a + 2)*x^9 + a*x^7 + (a + 2)*x^5 + x^4 + a*x^3 + (a + 1)*x^2 + (a + 2)*x + 1
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [12], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:85, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [13], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:86, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [14], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:86, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
0 ((x^28 + (a + 2)*x^20 + x^14 + (a + 1)*x^12 + (2*a + 1)*x^11 + (a + 2)*x^10 + a*x^8 + (a + 2)*x^6 + x^5 + a*x^4 + (a + 1)*x^3 + (a + 2)*x^2 + x)/(x^36 + (a + 2)*x^30 + 2*a*x^28 + x^27 + 2*a*x^18 + (a + 1)*x^12 + (a + 1)*x^10 + (2*a + 1)*x^9 + (2*a + 2)*x^6 + 2*x^4 + (2*a + 1)*x^3 + 2*a*x + 1))*y
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [15], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:87, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [16], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:87, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y
(A.diffn()).inv_cartier() ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [17], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:88, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y
(A.diffn()).is_regular_on_U0() False
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [18], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:88, in regular_drw_form(omega)

File <string>:206, in inv_cartier(omega)

AttributeError: 'NoneType' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx)
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y
(A.diffn()).is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [19], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:88, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:103, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [20], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:85, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:100, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lomega_aux.dx.teichmuller()*C.x.teichmuller().diffn() + omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() 0
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [21], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:86, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:101, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004laux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [22], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:86, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:101, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004laux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [23], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:87, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:102, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [24], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:88, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:103, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [25], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:89, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:104, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [26], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:89, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:104, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [27], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:90, in regular_drw_form(omega)

File <string>:104, in regular_form(omega)

ValueError: The form ((x^92 + (a - 1)*x^86 + (-a - 1)*x^84 + x^83 + (-a)*x^78 - x^76 + (-a - 1)*x^72 + (-a)*x^70 + a*x^69 + a*x^68 + x^67 + (a - 1)*x^66 + (-a - 1)*x^64 + (-a - 1)*x^63 + x^62 + (-a)*x^61 + (-a)*x^60 + a*x^59 + (a + 1)*x^58 + (-a + 1)*x^54 - x^52 + (a - 1)*x^51 - x^50 + (-a - 1)*x^49 - x^48 + a*x^45 + (-a - 1)*x^44 + a*x^43 + (-a)*x^42 + (-a - 1)*x^41 + (-a - 1)*x^40 + (a - 1)*x^39 + a*x^38 + x^37 + (-a - 1)*x^36 + (a + 1)*x^34 + (-a + 1)*x^33 + x^32 - x^31 + (-a - 1)*x^30 + (-a)*x^29 - x^28 + a*x^27 + x^26 + (a + 1)*x^25 + (a - 1)*x^24 + (a + 1)*x^23 + a*x^21 + a*x^20 + x^19 + (a - 1)*x^18 + x^17 + x^16 + (-a - 1)*x^15 + x^14 + (a - 1)*x^13 - x^12 - x^11 + a*x^10 + (-a + 1)*x^9 - x^8 + (-a + 1)*x^7 + (-a - 1)*x^6 + (-a - 1)*x^5 - x^4 + (-a - 1)*x^3 + x^2)/(x^99*y + (-a + 1)*x^93*y + a*x^91*y - x^90*y + (-a - 1)*x^87*y + x^85*y + (-a + 1)*x^84*y + (a + 1)*x^83*y + a*x^82*y + x^81*y + (a - 1)*x^45*y + (a + 1)*x^39*y + x^37*y + (-a + 1)*x^36*y + (-a)*x^33*y + (a - 1)*x^31*y + (a + 1)*x^30*y + a*x^29*y + x^28*y - x^27*y + x^21*y + (-a - 1)*x^19*y + (a + 1)*x^18*y + (-a + 1)*x^15*y + (-a)*x^13*y + (-a - 1)*x^12*y + (a - 1)*x^11*y - x^10*y + (-a - 1)*x^9*y + (-a - 1)*x^6*y + x^4*y + (-a + 1)*x^3*y + (a + 1)*x^2*y + a*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True True
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [28], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:90, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:105, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True True
aux == omega False
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [29], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:91, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:106, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True True
True False
aux == omega False
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [30], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:91, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:106, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True True
aux == omega False
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [1], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:91, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:106, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux == omega True
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True
True True
aux == omega False
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [2], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:92, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:107, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux == omega True
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True
True True
aux == omega False
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [3], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:92, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:107, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux == omega True
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True
True True
aux - omega  + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [4], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:92, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:107, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux == omega True
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() False
True True
aux - omega  + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [5], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:93, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:108, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.mult_by_p()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + a*x + 1 over Finite Field in a of size 3^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2 - x^2*f1[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: fct = C.x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lfct = C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: fct = C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l (fct^p).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l (fct^p).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l()(fct^p).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l(), (fct^p).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()), (fct^p).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7h(V((((a - 1)*x^2)/(x^3*y + a*x*y + y)) dx), dV([(x^3 + a*x + 1)*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7l = GF(p)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lGF(p)[?7h[?12l[?25h[?25l[?7lsage: F = GF(p)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(f, m)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, m)[?7h[?12l[?25h[?25l[?7lx, m)[?7h[?12l[?25h[?25l[?7l^, m)[?7h[?12l[?25h[?25l[?7l3, m)[?7h[?12l[?25h[?25l[?7l , m)[?7h[?12l[?25h[?25l[?7l-, m)[?7h[?12l[?25h[?25l[?7l , m)[?7h[?12l[?25h[?25l[?7lx, m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, m)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l = C.y[?7h[?12l[?25h[?25l[?7lsage: fct = C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lC =superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7lFGF(p)[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()), (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux == omega True
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() False
True True
aux - omega  + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [17], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:93, in regular_drw_form(omega)

File <string>:203, in inv_cartier(omega)

File <string>:108, in regular_form(omega)

ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
)

....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
 

....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
7

....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
 

....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
 

....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
7

....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
.

....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
 

....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega.curve

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: omega = (C.x)^(-1)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 













 [?7h[?12l[?25h[?25l[?7lomega = (C.x)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.curve[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.cartier()

[?7h[?12l[?25h[?2004l[?7h(1/x) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 









 [?7h[?12l[?25h[?25l[?7lomega.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = (C.x)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega = a*omega

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lomega = a*omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.cartier()

[?7h[?12l[?25h[?2004l[?7h(a/x) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbn[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.nth_root(p)

[?7h[?12l[?25h[?2004l[?7h2*a + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF = GF(p)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: F.cardinality()

[?7h[?12l[?25h[?2004l[?7h9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lsage: f

[?7h[?12l[?25h[?2004l[?7hx^3 + a*x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: f[2]

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: f[1]

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux == omega False
---------------------------------------------------------------------------
UnboundLocalError                         Traceback (most recent call last)
Cell In [27], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:85, in regular_drw_form(omega)

File <string>:27, in decomposition_omega0_hpdh(omega)

File <string>:70, in cartier(self)

UnboundLocalError: cannot access local variable 'polynomial_part' where it is not associated with a value
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
aux == omega True
aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega  + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0)
True
aux == omega True
aux.omega, fct (((a - 1)*x^36 + (-a - 1)*x^30 - x^28 + (a - 1)*x^27 - x^18 + a*x^12 + a*x^10 + (a + 1)*x^9 + (-a)*x^6 + (-a + 1)*x^4 + (a + 1)*x^3 - x + (a - 1))/y) dx (((a + 2)*x^19 + (a + 1)*x^13 + x^11 + (2*a + 1)*x^10 + 2*a*x^7 + (a + 2)*x^5 + (a + 1)*x^4 + x^2 + (a + 2)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega  + V((((a - 1)*x^45 + (a + 1)*x^39 + x^37 + (-a + 1)*x^36 + (-a)*x^33 + (a - 1)*x^31 + (a + 1)*x^30 + a*x^29 + x^28 + (a + 1)*x^27 + x^21 + (-a)*x^19 + a*x^18 + (-a + 1)*x^15 + (a + 1)*x^13 + x^12 + (-a - 1)*x^11 + (-a + 1)*x^10 + (-a - 1)*x^9 + (-a - 1)*x^7 + (-a + 1)*x^4 + a*x^2 + x + (a - 1))/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*a*x^57 + (2*a + 2)*x^39 + x^33 + a*x^30 + (a + 2)*x^21 + 2*a*x^15 + (2*a + 2)*x^12 + x^6 + 2*a*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((2*a*x^12 + 2*x^6 + (a + 1)*x^4 + 2*a*x^3) dy) + dV(0)
True
aux == omega True
aux.omega, fct ((x^63 + (a - 1)*x^57 + (-a)*x^55 + x^54 + a*x^45 + a*x^39 + (-a - 1)*x^37 + (a - 1)*x^36 + (-a - 1)*x^33 - x^31 + a*x^28 + a*x^27 + (a - 1)*x^21 + (a - 1)*x^19 + (-a + 1)*x^18 + (-a + 1)*x^15 + a*x^13 + (a - 1)*x^12 + (-a - 1)*x^10 + (a + 1)*x^9 + (-a - 1)*x^6 - x^4 + (-a + 1)*x^3 + (-a)*x + 1)/y) dx (((a + 1)*x^28 + (a + 2)*x^20 + (a + 1)*x^14 + (2*a + 1)*x^11 + (a + 2)*x^10 + 2*a*x^8 + (a + 1)*x^5 + 2*a*x^4 + (a + 2)*x^2 + (a + 1)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega  + V(((x^72 + (-a + 1)*x^66 + a*x^64 - x^63 + (-a - 1)*x^60 + x^58 + (-a + 1)*x^57 + (a + 1)*x^56 + a*x^55 + (a + 1)*x^54 + (a + 1)*x^48 + (a + 1)*x^46 + (-a - 1)*x^45 + (-a)*x^42 + (a + 1)*x^40 - x^39 + (-a + 1)*x^38 + x^37 + (a - 1)*x^36 + (a - 1)*x^34 + (-a - 1)*x^33 + a*x^32 + a*x^30 + (-a - 1)*x^29 + (a + 1)*x^28 + x^27 + a*x^24 + x^22 - x^21 - x^20 - x^19 + a*x^18 - x^16 - x^15 + (-a - 1)*x^14 + x^13 + a*x^12 + (-a + 1)*x^11 + (-a + 1)*x^10 - x^9 - x^8 + (a - 1)*x^7 + a*x^5 - x^4 + (a + 1)*x^2 + a*x + 1)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([(((2*a + 2)*x^84 + 2*a*x^60 + (2*a + 2)*x^42 + a*x^33 + 2*a*x^30 + (a + 2)*x^24 + (2*a + 2)*x^15 + (a + 2)*x^12 + 2*a*x^6 + (2*a + 2)*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((2*a*x^15 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6) dy) + dV(0)
True
aux == omega True
aux.omega, fct 0 dx ((x^13 + (a + 2)*x^7 + a*x^5 + x^4)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega  + V(((-x^11)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^39 + 2*a*x^21 + (2*a + 1)*x^15 + x^12)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((2*a*x^18 + 2*x^12 + (a + 1)*x^10 + 2*a*x^9) dy) + dV(0)
True
aux == omega True
aux.omega, fct (((a - 1)*x^54 + (-a - 1)*x^48 - x^46 + (a - 1)*x^45 + x^36 + x^30 + (-a)*x^28 + a*x^27 + (-a)*x^24 + (-a + 1)*x^22 + (a + 1)*x^21 - x^19 + (-a - 1)*x^18 + (-a - 1)*x^12 + (-a - 1)*x^10 + (a - 1)*x^9 + (a + 1)*x^6 + x^4 + (a - 1)*x^3 + a*x - 1)/y) dx (((a + 2)*x^25 + x^17 + (2*a + 1)*x^16 + (2*a + 1)*x^11 + (2*a + 2)*x^10 + x^8 + (a + 1)*x^7 + (2*a + 2)*x^5 + a*x^4 + (a + 2)*x^2 + (2*a + 2)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega  + V((((a - 1)*x^63 + (a + 1)*x^57 + x^55 + (-a + 1)*x^54 + (-a)*x^51 + (a - 1)*x^49 + (a + 1)*x^48 + a*x^47 + x^46 + a*x^45 + a*x^39 + a*x^37 + (a + 1)*x^36 - x^33 + a*x^31 + a*x^30 + (a + 1)*x^29 + (a + 1)*x^28 + x^27 + (-a - 1)*x^25 + (-a + 1)*x^22 + (-a)*x^21 + a*x^20 + (a - 1)*x^19 + x^18 + x^15 + (a - 1)*x^13 + (-a)*x^12 + (-a + 1)*x^11 + x^10 + (-a + 1)*x^9 + (-a + 1)*x^7 + x^4 + (-a - 1)*x^2 + (-a)*x - 1)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*a*x^75 + x^51 + a*x^48 + a*x^33 + (a + 1)*x^30 + x^24 + (2*a + 2)*x^21 + (a + 1)*x^15 + (2*a + 1)*x^12 + 2*a*x^6 + (a + 1)*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((2*a*x^30 + 2*x^24 + (a + 1)*x^22 + 2*a*x^21 + (a + 1)*x^12 + a*x^6 + (a + 2)*x^4 + (a + 1)*x^3) dy) + dV(0)
True
aux == omega True
aux.omega, fct 0 dx ((2*x^16 + (a + 2)*x^10 + 2*a*x^8 + 2*x^7 + (a + 1)*x^4 + 2*x^2 + (2*a + 1)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega  + V(((x^20 + (-a)*x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*x^48 + 2*a*x^30 + (a + 2)*x^24 + 2*x^21 + (2*a + 2)*x^12 + 2*x^6 + a*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((a*x^27 + x^21 + (2*a + 2)*x^19 + a*x^18 + (2*a + 2)*x^9 + 2*a*x^3 + (2*a + 1)*x + 2*a + 2) dy) + dV(0)
True
aux == omega True
aux.omega, fct 0 dx 0 True True
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega 0
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((0) dy) + dV(0)
True
aux == omega True
aux.omega, fct (((a - 1)*x^45 + (-a - 1)*x^39 - x^37 + (a - 1)*x^36 - x^27 + a*x^21 + a*x^19 + (a + 1)*x^18 + (-a)*x^15 + (-a + 1)*x^13 + (a + 1)*x^12 - x^10 + (a - 1)*x^9)/y) dx (((a + 2)*x^22 + (a + 1)*x^16 + x^14 + (2*a + 1)*x^13 + 2*a*x^10 + (a + 2)*x^8 + (a + 1)*x^7 + x^5 + (a + 2)*x^4)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False
mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True
True True
aux - omega  + V((((a - 1)*x^54 + (a + 1)*x^48 + x^46 + (-a + 1)*x^45 + (-a)*x^42 + (a - 1)*x^40 + (a + 1)*x^39 + a*x^38 + x^37 + (a + 1)*x^36 + x^30 + (-a)*x^28 + a*x^27 + (-a + 1)*x^24 + (a + 1)*x^22 + x^21 + (-a - 1)*x^20 + (-a + 1)*x^19 + (-a - 1)*x^18 + (-a - 1)*x^16 + (-a + 1)*x^13 + a*x^11 + x^10 + (a - 1)*x^9)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*a*x^66 + (2*a + 2)*x^48 + x^42 + a*x^39 + (a + 2)*x^30 + 2*a*x^24 + (2*a + 2)*x^21 + x^15 + 2*a*x^12)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y])
A.diffn().is_regular_on_U0() True
[0] d[x] + [0] d[y] + V((2*a*x^21 + 2*x^15 + (a + 1)*x^13 + 2*a*x^12) dy) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf[1][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF.cardinality()[?7h[?12l[?25h[?25l[?7lanth_root(p)[?7h[?12l[?25h[?25l[?7lomega.carier()[?7h[?12l[?25h[?25l[?7l = a*omega[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7l = (C.x)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lC =superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7lfct= C.y[?7h[?12l[?25h[?25l[?7lsage: fct = C.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m "naprawioney brak (1/p)-liniowosci cartiera)"
[master 1f66cae] naprawiony brak (1/p)-liniowosci cartiera
 6 files changed, 2428 insertions(+), 13 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 23, done.
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Counting objects: 100% (23/23), done.
Delta compression using up to 4 threads
Compressing objects:   8% (1/12)
Compressing objects:  16% (2/12)
Compressing objects:  25% (3/12)
Compressing objects:  33% (4/12)
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Compressing objects: 100% (12/12), done.
Writing objects:   8% (1/12)
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Writing objects: 100% (12/12), 14.29 KiB | 232.00 KiB/s, done.
Total 12 (delta 11), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   a5c2ce2..1f66cae  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ scd sage
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0)
True
[0] d[x] + [0] d[y] + V((2*a*x^12 + 2*x^6 + (a + 1)*x^4 + 2*a*x^3) dy) + dV(0)
True
[0] d[x] + [0] d[y] + V((2*a*x^15 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6) dy) + dV(0)
True
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
File <string>:59, in __mul__(self, other)

File <string>:260, in reduction(C, g)

File /ext/sage/9.8/src/sage/arith/misc.py:2021, in xgcd(a, b)
   2020 try:
-> 2021     return a.xgcd(b)
   2022 except AttributeError:

File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
   4496 if have_same_parent(self, other):
-> 4497     return method(self, other, *args, **kwargs)
   4498 else:

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:8931, in sage.rings.polynomial.polynomial_element.Polynomial.xgcd()
   8930 if hasattr(self.base_ring(), '_xgcd_univariate_polynomial'):
-> 8931     return self.base_ring()._xgcd_univariate_polynomial(self, other)
   8932 else:

File /ext/sage/9.8/src/sage/categories/fields.py:373, in Fields.ParentMethods._xgcd_univariate_polynomial(self, a, b)
    372 while v3:
--> 373     q, r = d.quo_rem(v3)
    374     (u, d, v1, v3) = (v1, v3, u - v1*q, r)

File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
   4496 if have_same_parent(self, other):
-> 4497     return method(self, other, *args, **kwargs)
   4498 else:

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:11734, in sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.quo_rem()
  11733 for k from m-n >= k >= 0:
> 11734     q = x[n+k-1] * inv
  11735     for j from n+k-2 >= j >= k:

File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
   1512 if HAVE_SAME_PARENT(cl):
-> 1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:670, in sage.rings.fraction_field_element.FractionFieldElement._mul_()
    669 d2 = snum.gcd(rden)
--> 670 if not d1.is_unit():
    671     rnum = rnum // d1

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:5544, in sage.rings.polynomial.polynomial_element.Polynomial.is_unit()
   5543     return self._parent._base.zero().is_unit()
-> 5544 return self.get_unsafe(0).is_unit()
   5545 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:180, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.get_unsafe()
    179 cdef ZZ_pE_c c_pE = ZZ_pEX_coeff(self.x, i)
--> 180 return self._parent._base(ZZ_pE_c_to_list(c_pE))
    181 

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    895 if no_extra_args:
--> 896     return mor._call_(x)
    897 else:

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.8/src/sage/rings/finite_rings/finite_field_givaro.py:230, in FiniteField_givaro._element_constructor_(self, e)
    228     return self._cache.random_element()
--> 230 def _element_constructor_(self, e):
    231     """
    232     Coerces several data types to ``self``.
    233 
   (...)
    369         2*a4^3 + 2*a4^2 + 1
    370     """

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Cell In [1], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:30

File <string>:82, in regular_drw_form(omega)

File <string>:99, in diffn(self, dy_w)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
   1959         return y
   1960 
-> 1961     return coercion_model.bin_op(left, right, operator.mul)
   1962 
   1963 cpdef _mul_(self, right):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:55, in __rmul__(self, other)

File <string>:84, in __add__(self, other)

File <string>:65, in __mul__(self, other)

File <string>:63, in __mul__(self, other)

AttributeError: 'superelliptic_function' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():

....:     print(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7l....:     print(mult_by_p(b.omega0).regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():

....:     print(mult_by_p(b.omega0).regular_form())

....: 

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [2], line 1
----> 1 for b in C1.de_rham_basis():
      2     print(mult_by_p(b.omega0).regular_form())

File <string>:123, in de_rham_basis(self)

File <string>:105, in basis_de_rham_degrees(self)

File <string>:5, in __init__(self, C, omega, fct)

File <string>:28, in __sub__(self, other)

File <string>:7, in __init__(self, C, g)

File <string>:296, in reduction_form(C, g)

File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
   1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
-> 1515     return coercion_model.bin_op(left, right, mul)
   1516 
   1517 cdef long value

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
   1198 # Now coerce to a common parent and do the operation there
   1199 try:
-> 1200     xy = self.canonical_coercion(x, y)
   1201 except TypeError:
   1202     self._record_exception()

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1313     x_elt = x
   1314 if y_map is not None:
-> 1315     y_elt = (<Map>y_map)._call_(y)
   1316 else:
   1317     y_elt = y

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:432, in sage.structure.coerce_maps.CallableConvertMap._call_()
    430         y = self._func(C, x)
    431     else:
--> 432         y = self._func(x)
    433 except Exception:
    434     if print_warnings:

File /ext/sage/9.8/src/sage/rings/fraction_field.py:324, in FractionField_generic._coerce_map_from_.<locals>.wrapper(x)
    323 def wrapper(x):
--> 324     return self._element_class(self, x.numerator(), x.denominator())

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1167, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
   1165     1/2/x
   1166 """
-> 1167 FractionFieldElement.__init__(self, parent, numerator, denominator,
   1168         coerce, reduce)
   1169 if not reduce:

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:121, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
    119 if reduce and parent.is_exact():
    120     try:
--> 121         self.reduce()
    122     except ArithmeticError:
    123         pass

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
   1237 if self._is_reduced:
   1238     return
-> 1239 super(self.__class__, self).reduce()
   1240 self.normalize_leading_coefficients()
   1241 

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    162     return codomain.coerce(nnum/nden)
    163 
--> 164 cpdef reduce(self):
    165     """
    166     Reduce this fraction.

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:210, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
    208 if not self.__denominator.is_one() and self.__denominator.is_unit():
    209     try:
--> 210         inv = self.__denominator.inverse_of_unit()
    211     except Exception:
    212         pass

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:1524, in sage.rings.polynomial.polynomial_element.Polynomial.inverse_of_unit()
   1522 else:
   1523     cst = self.get_unsafe(0)
-> 1524 inv = cst.inverse_of_unit()
   1525 return self._parent([inv])
   1526 

File /ext/sage/9.8/src/sage/categories/fields.py:817, in Fields.ElementMethods.inverse_of_unit(self)
    787 def inverse_of_unit(self):
    788     r"""
    789     Return the inverse of this element.
    790 
   (...)
    815         +infinity
    816     """
--> 817     return ~self

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:934, in sage.rings.fraction_field_element.FractionFieldElement.__invert__()
    932 if self.is_zero():
    933     raise ZeroDivisionError("Cannot invert 0")
--> 934 return self.__class__(self._parent,
    935     self.__denominator, self.__numerator, coerce=False, reduce=False)
    936 

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1170, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
   1168             coerce, reduce)
   1169     if not reduce:
-> 1170         self.normalize_leading_coefficients()
   1171 
   1172 cdef normalize_leading_coefficients(self):

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1177, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.normalize_leading_coefficients()
   1175 """
   1176 invlc = ~self.__denominator.leading_coefficient()
-> 1177 self.__denominator = self.__denominator.monic()
   1178 self.__numerator *= invlc
   1179 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:5724, in sage.rings.polynomial.polynomial_element.Polynomial.monic()
   5722 - Naqi Jaffery (2006-01-24): examples
   5723 """
-> 5724 if self.is_monic():
   5725     return self
   5726 a = ~self.leading_coefficient()

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:5497, in sage.rings.polynomial.polynomial_element.Polynomial.is_monic()
   5495     - Naqi Jaffery (2006-01-24): examples
   5496     """
-> 5497     return not self.is_zero() and self[self.degree()] == 1
   5498 
   5499 def is_unit(self):

File /ext/sage/9.8/src/sage/structure/element.pyx:1111, in sage.structure.element.Element.__richcmp__()
   1109         return (<Element>self)._richcmp_(other, op)
   1110     else:
-> 1111         return coercion_model.richcmp(self, other, op)
   1112 
   1113 cpdef _richcmp_(left, right, int op):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
   1971 # Coerce to a common parent
   1972 try:
-> 1973     x, y = self.canonical_coercion(x, y)
   1974 except (TypeError, NotImplementedError):
   1975     pass

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1313     x_elt = x
   1314 if y_map is not None:
-> 1315     y_elt = (<Map>y_map)._call_(y)
   1316 else:
   1317     y_elt = y

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.8/src/sage/rings/finite_rings/finite_field_givaro.py:230, in FiniteField_givaro._element_constructor_(self, e)
    212     """
    213     Return a random element of ``self``.
    214 
   (...)
    226         True
    227     """
    228     return self._cache.random_element()
--> 230 def _element_constructor_(self, e):
    231     """
    232     Coerces several data types to ``self``.
    233 
   (...)
    369         2*a4^3 + 2*a4^2 + 1
    370     """
    371     return self._cache.element_from_data(e)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():

....:     print(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7l....:     print(mult_by_p(b.omega0).regular_form())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():

....:     print(mult_by_p(b.omega0).regular_form())

....: 

[?7h[?12l[?25h[?2004lTrue
[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0)
True
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [3], line 2
      1 for b in C1.de_rham_basis():
----> 2     print(mult_by_p(b.omega0).regular_form())

File <string>:82, in regular_drw_form(omega)

File <string>:73, in diffn(self, dy_w)

File <string>:177, in dy_w(C)

File <string>:149, in auxilliary_derivative(P)

File <string>:149, in auxilliary_derivative(P)

File <string>:149, in auxilliary_derivative(P)

File <string>:147, in auxilliary_derivative(P)

File <string>:35, in __sub__(self, other)

File <string>:32, in __add__(self, other)

File <string>:39, in __add__(self, other)

File <string>:260, in reduction(C, g)

File /ext/sage/9.8/src/sage/arith/misc.py:2021, in xgcd(a, b)
   1933 r"""
   1934 Return a triple ``(g,s,t)`` such that `g = s\cdot a+t\cdot b = \gcd(a,b)`.
   1935 
   (...)
   2018     (1, 7*a^2/b^2, (((-h)*a)/b^2)*y + 1/b)
   2019 """
   2020 try:
-> 2021     return a.xgcd(b)
   2022 except AttributeError:
   2023     a = py_scalar_to_element(a)

File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
   4495 def new_method(self, other, *args, **kwargs):
   4496     if have_same_parent(self, other):
-> 4497         return method(self, other, *args, **kwargs)
   4498     else:
   4499         a, b = coercion_model.canonical_coercion(self, other)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:8931, in sage.rings.polynomial.polynomial_element.Polynomial.xgcd()
   8929 """
   8930 if hasattr(self.base_ring(), '_xgcd_univariate_polynomial'):
-> 8931     return self.base_ring()._xgcd_univariate_polynomial(self, other)
   8932 else:
   8933     raise NotImplementedError("%s does not provide an xgcd implementation for univariate polynomials"%self.base_ring())

File /ext/sage/9.8/src/sage/categories/fields.py:378, in Fields.ParentMethods._xgcd_univariate_polynomial(self, a, b)
    376 if d:
    377     c = ~d.leading_coefficient()
--> 378     d, u, v = c*d, c*u, c*v
    379 return d, u, v

File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
   1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
-> 1515     return coercion_model.bin_op(left, right, mul)
   1516 
   1517 cdef long value

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1194, in sage.structure.coerce.CoercionModel.bin_op()
   1192 if action is not None:
   1193     if (<Action>action)._is_left:
-> 1194         return (<Action>action)._act_(x, y)
   1195     else:
   1196         return (<Action>action)._act_(y, x)

File /ext/sage/9.8/src/sage/structure/coerce_actions.pyx:612, in sage.structure.coerce_actions.LeftModuleAction._act_()
    610 if self.extended_base is not None:
    611     a = <ModuleElement?>self.extended_base(a)
--> 612 return (<ModuleElement>a)._rmul_(<Element>g)  # g * a
    613 
    614 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:11518, in sage.rings.polynomial.polynomial_element.Polynomial_generic_dense._rmul_()
  11516 if c._parent is not (<Element>self.__coeffs[0])._parent:
  11517     c = (<Element>self.__coeffs[0])._parent.coerce(c)
> 11518 v = [c * a for a in self.__coeffs]
  11519 cdef Polynomial_generic_dense res = self._new_c(v, self._parent)
  11520 #if not v[len(v)-1]:

File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
   1511 cdef int cl = classify_elements(left, right)
   1512 if HAVE_SAME_PARENT(cl):
-> 1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
   1515     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:686, in sage.rings.fraction_field_element.FractionFieldElement._mul_()
    684         except NotImplementedError:
    685             pass
--> 686     return self.__class__(self._parent, tnum, tden,
    687         coerce=False, reduce=False)
    688 except AttributeError:

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1170, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
   1168             coerce, reduce)
   1169     if not reduce:
-> 1170         self.normalize_leading_coefficients()
   1171 
   1172 cdef normalize_leading_coefficients(self):

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1178, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.normalize_leading_coefficients()
   1176     invlc = ~self.__denominator.leading_coefficient()
   1177     self.__denominator = self.__denominator.monic()
-> 1178     self.__numerator *= invlc
   1179 
   1180 def is_integral(self):

File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
   1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
-> 1515     return coercion_model.bin_op(left, right, mul)
   1516 
   1517 cdef long value

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op()
   1194         return (<Action>action)._act_(x, y)
   1195     else:
-> 1196         return (<Action>action)._act_(y, x)
   1197 
   1198 # Now coerce to a common parent and do the operation there

File /ext/sage/9.8/src/sage/structure/coerce_actions.pyx:645, in sage.structure.coerce_actions.RightModuleAction._act_()
    643 if self.extended_base is not None:
    644     a = <ModuleElement?>self.extended_base(a)
--> 645 return (<ModuleElement>a)._lmul_(<Element>g)  # a * g
    646 
    647 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:221, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX._lmul_()
    219 r._parent = (<Polynomial_template>self)._parent
    220 r._cparent = (<Polynomial_template>self)._cparent
--> 221 d = self._parent._modulus.ZZ_pE(list(left.polynomial()))
    222 ZZ_pEX_mul_ZZ_pE(r.x, self.x, d.x)
    223 return r

File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx:154, in sage.libs.ntl.ntl_ZZ_pEContext.ntl_ZZ_pEContext_class.ZZ_pE()
    152     """
    153     from .ntl_ZZ_pE import ntl_ZZ_pE
--> 154     return ntl_ZZ_pE(v,modulus=self)
    155 
    156 def ZZ_pEX(self, v = None):

File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_pE.pyx:117, in sage.libs.ntl.ntl_ZZ_pE.ntl_ZZ_pE.__init__()
    115     self.x = ZZ_pX_to_ZZ_pE((<ntl_ZZ_pX>v).x)
    116 elif isinstance(v, (list, tuple)):
--> 117     tmp_zzpx = <ntl_ZZ_pX>ntl_ZZ_pX(v, self.c.pc)
    118     self.c.restore_c()   # allocating tmp_zzpx can change the current modulus trac #25790
    119     self.x = ZZ_pX_to_ZZ_pE(tmp_zzpx.x)

File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_pX.pyx:108, in sage.libs.ntl.ntl_ZZ_pX.ntl_ZZ_pX.__init__()
    106 for i, x in enumerate(v):
    107     if not isinstance(x, ntl_ZZ_p):
--> 108         cc = ntl_ZZ_p(x, self.c)
    109         self.c.restore_c()
    110     else:

File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_p.pyx:131, in sage.libs.ntl.ntl_ZZ_p.ntl_ZZ_p.__init__()
    129     ZZ_p_div(self.x, ZZ_to_ZZ_p(num), ZZ_to_ZZ_p(den))
    130 else:
--> 131     str_v = str(v)  # can cause modulus to change  trac #25790
    132     self.c.restore_c()
    133     ccreadstr(self.x, str_v)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0)
[0] d[x] + [0] d[y] + V((2*a*x^12 + 2*x^6 + (a + 1)*x^4 + 2*a*x^3) dy) + dV(0)
[0] d[x] + [0] d[y] + V((2*a*x^15 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6) dy) + dV(0)
[0] d[x] + [0] d[y] + V((2*a*x^18 + 2*x^12 + (a + 1)*x^10 + 2*a*x^9) dy) + dV(0)
[0] d[x] + [0] d[y] + V((2*a*x^30 + 2*x^24 + (a + 1)*x^22 + 2*a*x^21 + (a + 1)*x^12 + a*x^6 + (a + 2)*x^4 + (a + 1)*x^3) dy) + dV(0)
[0] d[x] + [0] d[y] + V((a*x^27 + x^21 + (2*a + 2)*x^19 + a*x^18 + (2*a + 2)*x^9 + 2*a*x^3 + (2*a + 1)*x + 2*a + 2) dy) + dV(0)
[0] d[x] + [0] d[y] + V((0) dy) + dV(0)
[0] d[x] + [0] d[y] + V((2*a*x^21 + 2*x^15 + (a + 1)*x^13 + 2*a*x^12) dy) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ccd ..cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git addd -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""u"s"u"n"i"e"t"e" "z"b"e"n""d"n"e" "k"o"m"u"n"i"k"a"t"y"
[master 5e738d4] usuniete zbedne komunikaty
 2 files changed, 604 insertions(+), 8 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 11, done.
Counting objects:   9% (1/11)
Counting objects:  18% (2/11)
Counting objects:  27% (3/11)
Counting objects:  36% (4/11)
Counting objects:  45% (5/11)
Counting objects:  54% (6/11)
Counting objects:  63% (7/11)
Counting objects:  72% (8/11)
Counting objects:  81% (9/11)
Counting objects:  90% (10/11)
Counting objects: 100% (11/11)
Counting objects: 100% (11/11), done.
Delta compression using up to 4 threads
Compressing objects:  16% (1/6)
Compressing objects:  33% (2/6)
Compressing objects:  50% (3/6)
Compressing objects:  66% (4/6)
Compressing objects:  83% (5/6)
Compressing objects: 100% (6/6)
Compressing objects: 100% (6/6), done.
Writing objects:  16% (1/6)
Writing objects:  33% (2/6)
Writing objects:  50% (3/6)
Writing objects:  66% (4/6)
Writing objects:  83% (5/6)
Writing objects: 100% (6/6)
Writing objects: 100% (6/6), 4.88 KiB | 72.00 KiB/s, done.
Total 6 (delta 5), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   1f66cae..5e738d4  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0 = omega.int()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: group

 group_action_matrices      group_action_matrices_log 

 group_action_matrices_dR   group_action_matrices_old 

 group_action_matrices_holo groups                    



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_action_matrices

 group_action_matrices     





 <unknown> [?7h[?12l[?25h[?25l[?7l_dR

 group_action_matrices     

 group_action_matrices_dR  [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_dR(C)

[?7h[?12l[?25h[?2004l[?7h[
[    1 a + 1     0     0     0     a]  [1 1 0 0 0 1]
[    0     1     0     0     0     0]  [0 1 0 0 0 0]
[    0     0     1     0     a     0]  [0 0 1 0 1 0]
[    0     0     0     1     1     0]  [0 0 0 1 a 0]
[    0     0     0     0     1     0]  [0 0 0 0 1 0]
[    0     0     0     0     0     1], [0 0 0 0 0 1]
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magma

 magma         magma_free   

 magma_console magmathis    





 [?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magma_this(A, B)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [4], line 1
----> 1 magma_this(A, B)

NameError: name 'magma_this' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagma_this(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magma_this(A, B)

 magma         magma_free   

 magma_console magmathis    





 [?7h[?12l[?25h[?25l[?7l

 magma        



 <unknown> [?7h[?12l[?25h[?25l[?7l_free

 magma         magma_free   [?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magma_free(A, B)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [5], line 1
----> 1 magma_free(A, B)

File /ext/sage/9.8/src/sage/misc/lazy_import.pyx:404, in sage.misc.lazy_import.LazyImport.__call__()
    402         True
    403     """
--> 404     return self.get_object()(*args, **kwds)
    405 
    406 def __repr__(self):

File /ext/sage/9.8/src/sage/interfaces/magma_free.py:85, in MagmaFree.__call__(self, code, strip, columns)
     84 def __call__(self, code, strip=True, columns=0):
---> 85     return magma_free_eval(code, strip=strip, columns=columns)

File /ext/sage/9.8/src/sage/interfaces/magma_free.py:45, in magma_free_eval(code, strip, columns)
     43 refererPath = "/calc/"
     44 refererUrl = "http://%s%s" % ( server, refererPath)
---> 45 code = "SetColumns(%s);\n"%columns + code
     46 params = urlencode({'input':code})
     47 headers = {"Content-type": "application/x-www-form-urlencoded",
     48            "Accept": "Accept: text/html, application/xml, application/xhtml+xml", "Referer": refererUrl}

TypeError: can only concatenate str (not "sage.matrix.matrix_gf2e_dense.Matrix_gf2e_dense") to str
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagma_free(A, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagma_free(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0 a^2]
[  0   1   1]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1 a^2   0]
[  0   1   0]
[  0   0   1],
[  1   1 a^2]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( (a*x^3) * dx, z1/x ), ( (x^3) * dx, z0/x ), ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ), ( (a*x^2) * dx, z1/x^2 ), ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   a]
[  0   1   0]
[  0   0   1],
[  1   0   0]
[  0   1   1]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1 a^2   a]
[  0   1   0]
[  0   0   1],
[  1   1   a]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.nth_root(p)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (a+1)/a

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A, B

[?7h[?12l[?25h[?2004l[?7h(
[    1 a + 1     0     0     0     a]  [1 1 0 0 0 1]
[    0     1     0     0     0     0]  [0 1 0 0 0 0]
[    0     0     1     0     a     0]  [0 0 1 0 1 0]
[    0     0     0     1     1     0]  [0 0 0 1 a 0]
[    0     0     0     0     1     0]  [0 0 0 0 1 0]
[    0     0     0     0     0     1], [0 0 0 0 0 1]
)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef sumka2(N):[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: dR = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l&[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: dR[1] + a*dR[5]

[?7h[?12l[?25h[?2004l[?7h( ((a + 1)*z1) * dx, a*z0*z1/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR[1] + a*dR[5][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(dR[1] + a*dR[5])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: (dR[1] + a*dR[5]).group_action([1, 0])

[?7h[?12l[?25h[?2004l[?7h( ((a + 1)*z1) * dx, (a*z0*z1 + a*z1)/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(dR[1] + a*dR[5]).group_action([1, 0])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR[1] + a*dR[5][?7h[?12l[?25h[?25l[?7lsage: (dR[1] + a*dR[5]).group_action([1, 0]) == dR[1] + a*dR[5]

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(dR[1] + a*dR[5]).group_action([1, 0]) == dR[1] + a*dR[5][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (dR[1] + a*dR[5]).group_action([1, 0]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 1, 0, 0, 0, a)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^2*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), ( (x^3*z0) * dx, z0*z1/x^3 ), ( (x^2*z0) * dx, z0*z1/x^4 )]
[1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1] [1 1 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^2*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), ( (x^3*z0) * dx, z0*z1/x^3 ), ( (x^2*z0) * dx, z0*z1/x^4 )]
[1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^2*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0 + z1) * dx, z0*z1/x^2 ), ( (x^3*z0) * dx, z0*z1/x^3 ), ( (x^2*z0) * dx, z0*z1/x^4 )]
[1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (x^5*z0) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^4*z0) * dx, z0*z1/x^2 ), ( (x^3) * dx, z1/x^3 ), ( (x^3*z0) * dx, z0*z1/x^3 )]
[1 1 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[    1 a + 1     0     0     0     a]
[    0     1     0     0     0     0]
[    0     0     1     0     a     0]
[    0     0     0     1     1     0]
[    0     0     0     0     1     0]
[    0     0     0     0     0     1] 
 [1 1 0 0 0 1]
[0 1 0 0 0 0]
[0 0 1 0 1 0]
[0 0 0 1 a 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0 a^2]
[  0   1   1]
[  0   0   1],
[  1   0   1]
[  0   1   0]
[  0   0   1]
}
{
[  1 a^2   0]
[  0   1   0]
[  0   0   1],
[  1   1 a^2]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( ((a + 1)*z0 + z1) * dx, 0 ), ( (x) * dx, 0 ), ( (0) * dx, z1/x ), ( (a*x*z0 + x*z1) * dx, z0*z1/x ), ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[    1 a + 1     0     0     0     a]
[    0     1     0     0     0     0]
[    0     0     1     0     a     0]
[    0     0     0     1     1     0]
[    0     0     0     0     1     0]
[    0     0     0     0     0     1] 
 [1 1 0 0 0 1]
[0 1 0 0 0 0]
[0 0 1 0 1 0]
[0 0 0 1 a 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0 a^2]
[  0   1   1]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1 a^2   a]
[  0   1   0]
[  0   0   1],
[  1   1   1]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( (a*x^3) * dx, z1/x ), ( (x^3) * dx, z0/x ), ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ), ( (a*x^2) * dx, z1/x^2 ), ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
[    1     0     1     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     1     0     1     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     1     0]
[    0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     1] 
 [1 1 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 a 0]
[0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 a 0]
[0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1 a^2   1]
[  0   1   0]
[  0   0   1],
[  1   1 a^2]
[  0   1   0]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   a]
[  0   0   1],
[  1   0   1]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   a]
[  0   1   0]
[  0   0   1],
[  1   0   0]
[  0   1   1]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^5
z1^2 - z1 = a*x^5

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.mult_by_p()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7lfC.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l=C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.f.coordinates()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7laluation[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.valuation()

[?7h[?12l[?25h[?2004l[?7h-8
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^4

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7lsage: ff.valuation()\

[?7h[?12l[?25h[?2004l[?7h-4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.valuation()\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.mult_by_p()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?7h[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z0*z1/x^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4) * dx, 0 ), ( (a*x^5) * dx, z1/x ), ( (x^5) * dx, z0/x ), ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ), ( (a*x^4) * dx, z1/x^2 ), ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ), ( (0) * dx, z1/x^3 ), ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ), ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), ( (x*z0) * dx, z0*z1/x^5 )]
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   1   a]
[  0   1   0]
[  0   0   1],
[  1 a^2   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   1]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   a]
[  0   0   1],
[  1   0   0]
[  0   1   a]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   1]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1 a^2   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.mult_bp()[?7h[?12l[?25h[?25l[?7le_rhamasis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 ((a + 1)*x*z0 + x*z1) * dx,
 (x^2) * dx,
 ((a + 1)*x^2*z0 + x^2*z1) * dx,
 (x^3) * dx,
 (x^4) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.valuation()\[?7h[?12l[?25h[?25l[?7lor b in C1.de_rham_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis():

....: [?7h[?12l[?25h[?25l[?7lprint(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(C.holomorphic_differentials_basis()[4].duality_pairing(b))

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis():

....:     print(C.holomorphic_differentials_basis()[4].duality_pairing(b))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [16], line 2
      1 for b in C.cohomology_of_structure_sheaf_basis():
----> 2     print(C.holomorphic_differentials_basis()[Integer(4)].duality_pairing(b))

AttributeError: 'as_form' object has no attribute 'duality_pairing'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis():

....:     print(C.holomorphic_differentials_basis()[4].duality_pairing(b))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[4][?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l....: 

....:         print()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]

()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(b.duality_pairing(om))

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis():

....:     om = C.holomorphic_differentials_basis()[4]

....:     print(b.duality_pairing(om))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [17], line 3
      1 for b in C.cohomology_of_structure_sheaf_basis():
      2     om = C.holomorphic_differentials_basis()[Integer(4)]
----> 3     print(b.duality_pairing(om))

AttributeError: 'as_function' object has no attribute 'duality_pairing'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller().
d

....: iffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + 2*C
1

....: .x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^47 + 3*
C

....: 1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + 2*C1.x^
1

....: 7 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^10
8

....:  + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74
 

....: + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x
^

....: 34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one)*C1.y.
d

....: iffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = C.holomorphic_differentials_basis()[4]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 













 [?7h[?12l[?25h[?25l[?7lom = C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier() == om8.cartir() + A.diffn()[?7h[?12l[?25h[?25l[?7l

 om.cartier               om.expansion             om.group_action          om.trace                

 om.coordinates           om.expansion_at_infty    om.residue               om.valuation            

 om.curve                 om.form                  om.serre_duality_pairing                         [?7h[?12l[?25h[?25l[?7lcartier

 om.cartier              





 <unknown> [?7h[?12l[?25h[?25l[?7loordinates

 om.cartier              

 om.coordinates          [?7h[?12l[?25h[?25l[?7lurve



 om.coordinates          

 om.curve                [?7h[?12l[?25h[?25l[?7l







[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lfor b in C.chomology_of_structure_heaf_basis():

....:     om = C.holomorphic_differentials_basis()[4]

....:     print(b.duality_pairing(om))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsduality_pairing(om)[?7h[?12l[?25h[?25l[?7leduality_pairing(om)[?7h[?12l[?25h[?25l[?7lrduality_pairing(om)[?7h[?12l[?25h[?25l[?7lrduality_pairing(om)[?7h[?12l[?25h[?25l[?7leduality_pairing(om)[?7h[?12l[?25h[?25l[?7l_duality_pairing(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis():

....:     om = C.holomorphic_differentials_basis()[4]

....:     print(b.serre_duality_pairing(om))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [19], line 3
      1 for b in C.cohomology_of_structure_sheaf_basis():
      2     om = C.holomorphic_differentials_basis()[Integer(4)]
----> 3     print(b.serre_duality_pairing(om))

AttributeError: 'as_function' object has no attribute 'serre_duality_pairing'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis():

....:     om = C.holomorphic_differentials_basis()[4]

....:     print(b.serre_duality_pairing(om))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7lb))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sere_duality_pairing(b)[?7h[?12l[?25h[?25l[?7lo.sere_duality_pairing(b)[?7h[?12l[?25h[?25l[?7lm.sere_duality_pairing(b)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(om.serre_duality_pairing(b))

....: [?7h[?12l[?25h[?25l[?7lsage: for b in C.cohomology_of_structure_sheaf_basis():

....:     om = C.holomorphic_differentials_basis()[4]

....:     print(om.serre_duality_pairing(b))

....: 

[?7h[?12l[?25h[?2004l0
0
0
a + 1
a
0
0
0
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()[3]

[?7h[?12l[?25h[?2004l[?7hz1/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[3][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[3][?7h[?12l[?25h[?25l[?7l()[3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()[4]

[?7h[?12l[?25h[?2004l[?7hz0*z1/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((a + 1)*x*z0 + x*z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x^2*z1 + x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (0) * dx, z1/x ), ( (x^5) * dx, z0/x ), ( (x^5*z1 + x^4 + x^3*z0) * dx, z0*z1/x ), ( (x^2) * dx, z1/x^2 ), ( (x^4) * dx, z0/x^2 ), ( (x^4*z1 + x^2*z0) * dx, z0*z1/x^2 ), ( (x^3*z1 + x^2*z1) * dx, z0*z1/x^3 ), ( (x^2*z1 + z0) * dx, z0*z1/x^4 )]
[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[4][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x*z1) * dx,
 (x^2*z1 + x*z0) * dx,
 (x^2) * dx,
 (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lz)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.z[1] + C.z[0])

[?7h[?12l[?25h[?2004l[?7hx*z1 + z0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.z[1] + C.z[0])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.z[1] + C.z[0]).valuation()

[?7h[?12l[?25h[?2004l[?7h-9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.z[1] + C.z[0]).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.z[1]).valuation()

[?7h[?12l[?25h[?2004l[?7h-14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different

 C.exponent_of_different     

 C.exponent_of_different_prim





 [?7h[?12l[?25h[?25l[?7l

 C.exponent_of_different     



 <unknown> [?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different()

[?7h[?12l[?25h[?2004l[?7h22
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC.exponent_of_different()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_()[?7h[?12l[?25h[?25l[?7lp()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lm()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h19
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (x^3*z1 + z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z1) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4) * dx, 0 ), ( (0) * dx, z1/x ), ( (x^7) * dx, z0/x ), ( (x^7*z1 + x*z0) * dx, z0*z1/x ), ( (x^6) * dx, z0/x^2 ), ( (x^6*z1 + z0) * dx, z0*z1/x^2 ), ( (x^5) * dx, z0/x^3 ), ( (x^5*z1) * dx, z0*z1/x^3 ), ( (x^4*z1) * dx, z0*z1/x^4 ), ( (x^3*z1) * dx, z0*z1/x^5 )]
[1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholmorphicials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (x^3*z1 + z0) * dx,
 (x) * dx,
 (x*z1) * dx,
 (x^2) * dx,
 (x^2*z1) * dx,
 (x^3) * dx,
 (x^4) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9
z1^2 - z1 = x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(M-m)+ 3/2*(M-m)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: M = 9

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7l = 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: m = 3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(M-m)+ 3/2*(M-m)[?7h[?12l[?25h[?25l[?7lsage: (M-m)+ 3/2*(M-m)

[?7h[?12l[?25h[?2004l[?7h15
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx.mult_by_p()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different()

[?7h[?12l[?25h[?2004l[?7h24
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.exponent_of_different()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_t()[?7h[?12l[?25h[?25l[?7lpt()[?7h[?12l[?25h[?25l[?7lrt()[?7h[?12l[?25h[?25l[?7lit()[?7h[?12l[?25h[?25l[?7lmt()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h21
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 3[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: m+2*M

[?7h[?12l[?25h[?2004l[?7h21
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm+2*M[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: m+2*M + 3

[?7h[?12l[?25h[?2004l[?7h24
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld.mult_by_p()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation()

[?7h[?12l[?25h[?2004l[?7h16
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(M-m)+ 3/2*(M-m)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lM)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (m+2*M - 3)/2

[?7h[?12l[?25h[?2004l[?7h9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x^2*z0 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx,
 (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().int()







































 [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: h1.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lsage: h1.diffn().regular_form().int()

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

 







































 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = 9[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l[?7h9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





































 [?7h[?12l[?25h[?25l[?7lm+2*M + 3[?7h[?12l[?25h[?25l[?7lsage: m

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

































 [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^5
z1^2 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 























 [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx.valuaton()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation()

[?7h[?12l[?25h[?2004l[?7h14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 



















 [?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: 5+14 - 5

[?7h[?12l[?25h[?2004l[?7h14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 















 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 













 [?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( ((a + 1)*z0 + z1) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
 ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[4][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[4][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?7h[z1/x, z0*z1/x, z0*z1/x^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.r()[?7h[?12l[?25h[?25l[?7lsage: x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x.divides(x^2)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (most recent call last):

  File /ext/sage/9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/IPython/core/interactiveshell.py:3433 in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

  Cell In [57], line 1
    load('init.sage')

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.8/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:32

  File sage/misc/persist.pyx:175 in sage.misc.persist.load
    sage.repl.load.load(filename, globals())

  File /ext/sage/9.8/src/sage/repl/load.py:272 in load
    exec(preparse_file(f.read()) + "\n", globals)

  File <string>:24
    print(result == )
                    ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.8/src/sage/structure/element.pyx:1970, in sage.structure.element.Element._mod_()
   1969 try:
-> 1970     python_op = (<object>self)._mod_
   1971 except AttributeError:

File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    493 """
--> 494 return self.getattr_from_category(name)
    495 

File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    506     cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
    508 

File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr

AttributeError: 'InfinityRing_class_with_category' object has no attribute '__custom_name'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Cell In [58], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:13

File <string>:45, in __init__(self, C, list_of_fcts, branch_points, prec)

File <string>:185, in artin_schreier_transform(power_series, prec)

File /ext/sage/9.8/src/sage/structure/element.pyx:1939, in sage.structure.element.Element.__mod__()
   1937     return (<Element>left)._mod_(right)
   1938 if BOTH_ARE_ELEMENT(cl):
-> 1939     return coercion_model.bin_op(left, right, mod)
   1940 
   1941 try:

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
   1202     self._record_exception()
   1203 else:
-> 1204     return PyObject_CallObject(op, xy)
   1205 
   1206 if op is mul:

File /ext/sage/9.8/src/sage/structure/element.pyx:1937, in sage.structure.element.Element.__mod__()
   1935 cdef int cl = classify_elements(left, right)
   1936 if HAVE_SAME_PARENT(cl):
-> 1937     return (<Element>left)._mod_(right)
   1938 if BOTH_ARE_ELEMENT(cl):
   1939     return coercion_model.bin_op(left, right, mod)

File /ext/sage/9.8/src/sage/structure/element.pyx:1972, in sage.structure.element.Element._mod_()
   1970     python_op = (<object>self)._mod_
   1971 except AttributeError:
-> 1972     raise bin_op_exception('%', self, other)
   1973 else:
   1974     return python_op(other)

TypeError: unsupported operand parent(s) for %: 'The Infinity Ring' and 'The Infinity Ring'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In [59], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:20

File <string>:344, in cohomology_of_structure_sheaf_basis(self, threshold)

File <string>:344, in <listcomp>(.0)

File <string>:131, in serre_duality_pairing(self, fct)

File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
    583     return expression.sum(*args, **kwds)
    584 elif max(len(args),len(kwds)) <= 1:
--> 585     return sum(expression, *args, **kwds)
    586 else:
    587     from sage.symbolic.ring import SR

File <string>:131, in <genexpr>(.0)

File <string>:124, in residue(self, place)

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue()
    616         Integer Ring
    617     """
--> 618     return self[-1]
    619 
    620 def exponents(self):

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
True
True
I haven't found all forms, only  16  of  18
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [60], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:20

File <string>:318, in cohomology_of_structure_sheaf_basis(self, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
True
True
True
True
True
True
True
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:281, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    280 try:
--> 281     if a.parent() is not K:
    282         a = K.coerce(a)

AttributeError: 'tuple' object has no attribute 'parent'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Cell In [61], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:13

File <string>:45, in __init__(self, C, list_of_fcts, branch_points, prec)

File <string>:196, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:284, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    282         a = K.coerce(a)
    283 except (TypeError, AttributeError, NotImplementedError):
--> 284     return Polynomial.__call__(self, a)
    285 
    286 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:904, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    902             return result
    903         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 904     return pol._compiled.eval(a)
    905 
    906 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (55 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (54 times)]

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
   1511 cdef int cl = classify_elements(left, right)
   1512 if HAVE_SAME_PARENT(cl):
-> 1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
   1515     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
    911 cdef LaurentSeries right = <LaurentSeries>right_r
    912 return type(self)(self._parent,
--> 913                   self.__u * right.__u,
    914                   self.__n + right.__n)
    915 

File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
   1511 cdef int cl = classify_elements(left, right)
   1512 if HAVE_SAME_PARENT(cl):
-> 1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
   1515     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
    538 """
    539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
    541                         self.__f * (<PowerSeries_poly>right_r).__f,
    542                         prec=prec,

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
     42     ValueError: series has negative valuation
     43 """
---> 44 R = parent._poly_ring()
     45 if isinstance(f, Element):
     46     if (<Element>f)._parent is R:

File /ext/sage/9.8/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
    958         pass
    959     return False
--> 961 def _poly_ring(self):
    962     """
    963     Return the underlying polynomial ring used to represent elements of
    964     this power series ring.
   (...)
    970         Univariate Polynomial Ring in t over Integer Ring
    971     """
    972     return self.__poly_ring

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
True
True
True
True
True
True
True
True
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( ((a + 1)*x*z0 + x*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (a*x^5) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ),
 ( (a*x^4) * dx, z1/x^2 ),
 ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ),
 ( (0) * dx, z1/x^3 ),
 ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ),
 ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ),
 ( (x*z0) * dx, z0*z1/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A, B

[?7h[?12l[?25h[?2004l[?7h(
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1],

[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x^2*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^5) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^5*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^4) * dx, z1/x^2 ),
 ( (x^4*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x^3*z0) * dx, z0*z1/x^3 ),
 ( (x^2*z0) * dx, z0*z1/x^4 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(m, M) + type1(m, M) + type2(m, M) + type3(m, M)[?7h[?12l[?25h[?25l[?7lC.x*C.z[1]).valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm(C.x)^(-1)[?7h[?12l[?25h[?25l[?7l(C.x)^(-1)[?7h[?12l[?25h[?25l[?7lo(C.x)^(-1)[?7h[?12l[?25h[?25l[?7lm(C.x)^(-1)[?7h[?12l[?25h[?25l[?7l (C.x)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l= (C.x)^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om= (C.x)^(-1)*C.z[1]*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom= (C.x)^(-1)*C.z[1]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier) == om8.cartier() + A.diffn()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.valuation()

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C); A, B

[?7h[?12l[?25h[?2004l[?7h(
[1 0 1 0 0 0 0 0 0 0 0 0 0 0]  [1 1 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]  [0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]  [0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0]  [0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]  [0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 1 0 0 0 0 0 0 0 1]  [0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 1 0]  [0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0]  [0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0]  [0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]  [0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0]  [0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]  [0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]  [0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0 0 0 0 1]
)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^5) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ),
 ( (x^4) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^4 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leC.de_rham_basis()[?7h[?12l[?25h[?25l[?7ltC.de_rham_basis()[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: eta[-2] + eta[4]

[?7h[?12l[?25h[?2004l[?7h( (x^3*z0 + x*z1) * dx, z0*z1/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta[4].group_action([0, 1]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta[4].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l-2] + eta[4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lteta[-2] + eta[4][?7h[?12l[?25h[?25l[?7laeta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l2eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l4eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l=eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta24 = eta[-2] + eta[4]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24 = eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l[4].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[4.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l2.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l4.group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta24.group_action([0, 1]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^5
z1^2 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^5) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ),
 ( (x^4) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^4 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l= C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: eta = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7limport itertools[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lsage: is

 is                           is_commutative               is_fundamental_discriminant  is_pAdicField                is_prime                     is_real_place                isinstance                  

 is_M32                       is_even                      is_integrally_closed         is_pAdicRing                 is_prime_power               is_square                    isogeny_codomain_from_kernel

 is_ProductProjectiveSpaces   is_field                     is_iterator                  is_package_installed         is_pseudoprime               is_squarefree                isqrt                       

 is_ProjectiveSpace           is_final                     is_odd                       is_power_of_two              is_pseudoprime_power         is_triangular_number         issubclass                  

 [?7h[?12l[?25h[?25l[?7l

 is                          







 <unknown> [?7h[?12l[?25h[?25l[?7lis_M32

 is                          

 is_M32                      [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l24.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l = eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7l= eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lsage: eta24 = eta[-2] + eta[4]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7leta24 = eta[-2] + eta[4][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: eta24

[?7h[?12l[?25h[?2004l[?7h( (x^3*z0 + x*z1) * dx, z0*z1/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lisM[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7lM32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta24)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta24)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-3])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-3])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l6])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-6])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-6])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[0])

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l4])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[4])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def gene(x):

....:     y1 = x - x.group_action([0, 1])

....:     y2 = x - x.group_action([1, 0])

....:     print(y1, y2)[?7h[?12l[?25h[?25l[?7l....:     print(y1, y2)

....: [?7h[?12l[?25h[?25l[?7lsage: def gene(x):

....:     y1 = x - x.group_action([0, 1])

....:     y2 = x - x.group_action([1, 0])

....:     print(y1, y2)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus(5, 7)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(eta[-1])

[?7h[?12l[?25h[?2004l( (1) * dx, z0/x^4 ) ( (x^2) * dx, z1/x^4 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-1])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gene(eta24)

[?7h[?12l[?25h[?2004l( (x) * dx, z0/x^3 ) ( (x^3) * dx, z1/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h8
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta24)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[-1])[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(eta[-3])

[?7h[?12l[?25h[?2004l( (x^2) * dx, z0/x^2 ) ( (x^4) * dx, z1/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[    1 a + 1     0     0     0     a]
[    0     1     0     0     0     0]
[    0     0     1     0     a     0]
[    0     0     0     1     1     0]
[    0     0     0     0     1     0]
[    0     0     0     0     0     1] 
 [1 1 0 0 0 1]
[0 1 0 0 0 0]
[0 0 1 0 1 0]
[0 0 0 1 a 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( ((a + 1)*z0 + z1) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
 ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[4])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lisM[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(eta[4])[?7h[?12l[?25h[?25l[?7lM32(eta[4])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l-])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-2])

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta24[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: eta = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-2])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0 a^2]
[  0   1 a^2]
[  0   0   1],
[  1   0   a]
[  0   1 a^2]
[  0   0   1]
}
{
[  1 a^2 a^2]
[  0   1   0]
[  0   0   1],
[  1   1 a^2]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lvaluation(305)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: v1 = vector((1, 0))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = vector((1, 0))[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: v2 = vector((2, 0))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv2 = vector((2, 0))[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: v1.

  v1.Mod                     v1.base_ring               v1.coefficient             v1.coordinate_ring         v1.degree                  v1.derivative              
 

  v1.additive_order          v1.cartesian_product       v1.coefficients            v1.cross_product           v1.denominator             v1.dict                    
 

  v1.apply_map               v1.category                v1.column                  v1.cross_product_matrix    v1.dense_coefficient_list  v1.diff                    
>

  v1.base_extend             v1.change_ring             v1.conjugate               v1.curl                    v1.dense_vector            v1.div                     
 

 [?7h[?12l[?25h[?25l[?7lMod

 v1.Mod                    







 <unknown> [?7h[?12l[?25h[?25l[?7lbase_ring

 v1.Mod                     v1.base_ring              [?7h[?12l[?25h[?25l[?7lcoefficient

 v1.base_ring               v1.coefficient            [?7h[?12l[?25h[?25l[?7lordnate_ring

 v1.coefficient             v1.coordinate_ring        [?7h[?12l[?25h[?25l[?7ldegee

 v1.coordinate_ring         v1.degree                 [?7h[?12l[?25h[?25l[?7lrivative

 v1.degree                  v1.derivative             [?7h[?12l[?25h[?25l[?7lot_product

 base_ringcoefficientordnate_ringdegee         rivativeot_product

 cartesian_productoefficients     ross_productdenominator  ict       ump

<category olumn  ross_product_matrixdenecoefficien_listiff                  umps

 chang_rigonjugate  url     dense_vectoriv         element[?7h[?12l[?25h[?25l[?7lge

coefficientordnate_ringdegee         rivativeot_productge        

oefficients     ross_productdenominator  ict       umphaming_weight

olumn  ross_product_matrixdenecoefficien_listiff                  umpshermitian_inner_product

onjugate  url     dense_vectoriv         elementinner_product[?7h[?12l[?25h[?25l[?7l

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsum(floor(305/5^n) for n in range(1, 10))[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: span(v1, v2)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [48], line 1
----> 1 span(v1, v2)

File /ext/sage/9.8/src/sage/modules/free_module.py:734, in span(gens, base_ring, check, already_echelonized)
    731     raise TypeError("generators must be given as an iterable structure")
    733 if R not in PrincipalIdealDomains():
--> 734     raise TypeError("The base_ring (= %s) must be a principal ideal "
    735                     "domain." % R)
    736 if not gens:
    737     return FreeModule(R, 0)

TypeError: The base_ring (= (2, 0)) must be a principal ideal domain.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: V = QQ^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV = QQ^2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: V.linear_

 V.linear_combination         

 V.linear_combination_of_basis

 V.linear_dependence          



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcombination

 V.linear_combination         





 <unknown> [?7h[?12l[?25h[?25l[?7l_of_basis

 V.linear_combination         

 V.linear_combination_of_basis[?7h[?12l[?25h[?25l[?7ldependence



 V.linear_combination_of_basis

 V.linear_dependence          [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v2])

[?7h[?12l[?25h[?2004l[?7h[
(2, -1)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv2 = vector((2, 0))[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: v3 = vector((2, 0))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 0))[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v2])

[?7h[?12l[?25h[?2004l[?7h[
(2, -1)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l3])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v3])

[?7h[?12l[?25h[?2004l[?7h[
(2, -1)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 0))[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v2])[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 0))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v3 = vector((2, 1))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 1))[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v3])

[?7h[?12l[?25h[?2004l[?7h[

]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def is_M32(x):

....:     n = len(x.coordinates())

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     if y1.coordinates() == vector(n*[0]):

....:         return False

....:     if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates():

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     if y2.coordinates() == vector(n*[0]):

....:         return False

....:     if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates():

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence(y1.coordinates(), y2.coordinates())) > 0:

....:         return False

....:     return True[?7h[?12l[?25h[?25l[?7l....:     return True

....: [?7h[?12l[?25h[?25l[?7lsage: def is_M32(x):

....:     n = len(x.coordinates())

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     if y1.coordinates() == vector(n*[0]):

....:         return False

....:     if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates():

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     if y2.coordinates() == vector(n*[0]):

....:         return False

....:     if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates():

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence(y1.coordinates(), y2.coordinates())) > 0:

....:         return False

....:     return True

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l32(eta[-1])[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [57], line 1
----> 1 is_M32(eta[-Integer(1)])

Cell In [56], line 15, in is_M32(x)
     13     return False
     14 V = F**n
---> 15 if len(V.linear_dependence(y1.coordinates(), y2.coordinates())) > Integer(0):
     16     return False
     17 return True

File /ext/sage/9.8/src/sage/modules/free_module.py:5026, in FreeModule_generic_field.linear_dependence(self, vectors, zeros, check)
   5024     for v in vectors:
   5025         if v not in self:
-> 5026             raise ValueError('vector %s is not an element of %s' % (v, self))
   5027 if zeros == 'left':
   5028     basis = 'echelon'

ValueError: vector 1 is not an element of Vector space of dimension 6 over Finite Field in a of size 2^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def is_M32(x):

....:     n = len(x.coordinates())

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     if y1.coordinates() == vector(n*[0]):

....:         return False

....:     if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates():

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     if y2.coordinates() == vector(n*[0]):

....:         return False

....:     if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates():

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1.coordinates(), y2.coordinates()])) > 0:

....:         return False

....:     return True[?7h[?12l[?25h[?25l[?7l....:     return True

....: [?7h[?12l[?25h[?25l[?7lsage: def is_M32(x):

....:     n = len(x.coordinates())

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     if y1.coordinates() == vector(n*[0]):

....:         return False

....:     if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates():

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     if y2.coordinates() == vector(n*[0]):

....:         return False

....:     if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates():

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1.coordinates(), y2.coordinates()])) > 0:

....:         return False

....:     return True

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def is_M32(x):

....:     n = len(x.coordinates())

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     if y1.coordinates() == vector(n*[0]):

....:         return False

....:     if y1.group_action([0, 1]).coordinates() != y1.coordinates() or y1.group_action([1, 0]).coordinates() != y1.coordinates():

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     if y2.coordinates() == vector(n*[0]):

....:         return False

....:     if y2.group_action([0, 1]).coordinates() != y2.coordinates() or y2.group_action([1, 0]).coordinates() != y2.coordinates():

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1.coordinates(), y2.coordinates()])) > 0:

....:         return False

....:     return True[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1])

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



























 [?7h[?12l[?25h[?25l[?7lis_M32(eta[-1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-2])

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 























 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
False
False
False
False
True
False
False
False
False
False
True
False
False
True
False
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ lolosage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[    1 a + 1     0     0     0     a]
[    0     1     0     0     0     0]
[    0     0     1     0     a     0]
[    0     0     0     1     1     0]
[    0     0     0     0     1     0]
[    0     0     0     0     0     1] 
 [1 1 0 0 0 1]
[0 1 0 0 0 0]
[0 0 1 0 1 0]
[0 0 0 1 a 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
False
False
False
False
True
False
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[    1     0     1     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     1     0     1     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     1     0]
[    0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     1] 
 [1 1 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 a 0]
[0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 a 0]
[0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1]
False
False
False
False
False
False
False
False
^C---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2080, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__()
   2079     # Attempt evaluation via singular.
-> 2080     coerced_x = [parent.coerce(e) for e in x]
   2081 except TypeError:

File /ext/sage/9.8/src/sage/structure/parent.pyx:1212, in sage.structure.parent.Parent.coerce()
   1211             _record_exception()
-> 1212     raise TypeError(_LazyString("no canonical coercion from %s to %s", (parent(x), self), {}))
   1213 else:

TypeError: no canonical coercion from Laurent Series Ring in t over Finite Field in a of size 2^2 to Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field in a of size 2^2

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Cell In [2], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:48

File <string>:29, in is_M32(x)

File <string>:54, in coordinates(self, threshold, basis)

File <string>:392, in de_rham_basis(self, threshold)

File <string>:371, in lift_to_de_rham(self, fct, threshold)

File <string>:136, in holomorphic_differentials_basis(self, threshold)

File <string>:61, in expansion(self, pt)

File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.8/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs()
    832         else:
    833             variables.append(gen)
--> 834     return self(*variables)
    835 
    836 def numerical_approx(self, prec=None, digits=None, algorithm=None):

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__()
    447         (-2*x1*x2 + x1 + 1)/(x1 + x2)
    448     """
--> 449     return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds)
    450 
    451 def _is_atomic(self):

File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2085, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__()
   2083 y = parent.base_ring().zero()
   2084 for (m,c) in self.dict().iteritems():
-> 2085     y += c*mul([ x[i]**m[i] for i in m.nonzero_positions()])
   2086 return y
   2087 

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:953, in sage.rings.laurent_series_ring_element.LaurentSeries.__pow__()
    951 if right.denominator() == 1:
    952     right = right.numerator()
--> 953     return type(self)(self._parent, self.__u**right, self.__n*right)
    954 
    955 if self.is_zero():

File /ext/sage/9.8/src/sage/rings/power_series_ring_element.pyx:1152, in sage.rings.power_series_ring_element.PowerSeries.__pow__()
   1150 if right.denominator() == 1:
   1151     right = right.numerator()
-> 1152     return super().__pow__(right, dummy)
   1153 
   1154 if self.is_zero():

File /ext/sage/9.8/src/sage/structure/element.pyx:2058, in sage.structure.element.Element.__pow__()
   2056     return (<Element>left)._pow_(right)
   2057 if BOTH_ARE_ELEMENT(cl):
-> 2058     return coercion_model.bin_op(left, right, pow)
   2059 
   2060 cdef long value

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op()
   1194         return (<Action>action)._act_(x, y)
   1195     else:
-> 1196         return (<Action>action)._act_(y, x)
   1197 
   1198 # Now coerce to a common parent and do the operation there

File /ext/sage/9.8/src/sage/structure/coerce_actions.pyx:892, in sage.structure.coerce_actions.IntegerPowAction._act_()
    890 integer_check_long(n, &value, &err)
    891 if not err:
--> 892     return e._pow_long(value)
    893 return e._pow_int(n)
    894 

File /ext/sage/9.8/src/sage/structure/element.pyx:2135, in sage.structure.element.Element._pow_long()
   2133 Generic path for powering with a C long.
   2134 """
-> 2135 return self._pow_int(n)
   2136 
   2137 

File /ext/sage/9.8/src/sage/structure/element.pyx:2712, in sage.structure.element.RingElement._pow_int()
   2710         OverflowError: exponent overflow (670592745)
   2711     """
-> 2712     return arith_generic_power(self, n)
   2713 
   2714 def powers(self, n):

File /ext/sage/9.8/src/sage/arith/power.pyx:83, in sage.arith.power.generic_power()
     81     raise NotImplementedError("non-integral exponents not supported")
     82 if not err:
---> 83     return generic_power_long(a, value)
     84 
     85 if n < 0:

File /ext/sage/9.8/src/sage/arith/power.pyx:102, in sage.arith.power.generic_power_long()
    100     u = -u
    101     a = invert(a)
--> 102 return generic_power_pos(a, u)
    103 
    104 

File /ext/sage/9.8/src/sage/arith/power.pyx:123, in sage.arith.power.generic_power_pos()
    121 apow *= apow
    122 if n & 1:
--> 123     res = apow * res
    124 n >>= 1
    125 

File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
   1511 cdef int cl = classify_elements(left, right)
   1512 if HAVE_SAME_PARENT(cl):
-> 1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
   1515     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
    538 """
    539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
    541                         self.__f * (<PowerSeries_poly>right_r).__f,
    542                         prec=prec,

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
     42     ValueError: series has negative valuation
     43 """
---> 44 R = parent._poly_ring()
     45 if isinstance(f, Element):
     46     if (<Element>f)._parent is R:

File /ext/sage/9.8/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
    958         pass
    959     return False
--> 961 def _poly_ring(self):
    962     """
    963     Return the underlying polynomial ring used to represent elements of
    964     this power series ring.
   (...)
    970         Univariate Polynomial Ring in t over Integer Ring
    971     """
    972     return self.__poly_ring

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( ((a + 1)*x*z0 + x*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (a*x^3) * dx, z1/x ),
 ( (x^3) * dx, z0/x ),
 ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ),
 ( (a*x^2) * dx, z1/x^2 ),
 ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor m in range(1, 20):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li2):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l8][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 8, 10, 11]:

....: [?7h[?12l[?25h[?25l[?7lprint(y1, y2)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(b))[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7l....:     print(is_

  is_M32                      is_commutative              is_final                    is_iterator                 is_pAdicRing                 

  is_ProductProjectiveSpaces  is_even                     is_fundamental_discriminant is_odd                      is_package_installed        >

  is_ProjectiveSpace          is_field                    is_integrally_closed        is_pAdicField               is_power_of_two              

 [?7h[?12l[?25h[?25l[?7lM32

 is_M32                     





 <unknown> [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.r().regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomolgy_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lfor i in [4, 8, 10, 11]:

....: ....:     print(is_M32(C.de_rham_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 8, 10, 11]:

....: ....:     print(is_M32(B[i]))

....: 

[?7h[?12l[?25h[?2004lFalse
True
True
False
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[0].omga0.r().regular_form()[?7h[?12l[?25h[?25l[?7l1egular_fom()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([1, 0]) - B[11]

[?7h[?12l[?25h[?2004l[?7h( (x) * dx, z1/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([1, 0]) - B[11][?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( ((a + 1)*x*z0 + x*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (a*x^3) * dx, z1/x ),
 ( (x^3) * dx, z0/x ),
 ( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x ),
 ( (a*x^2) * dx, z1/x^2 ),
 ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[11].group_action([1, 0]) - B[11][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l]) - B[1][?7h[?12l[?25h[?25l[?7l0]) - B[1][?7h[?12l[?25h[?25l[?7l,]) - B[1][?7h[?12l[?25h[?25l[?7l ]) - B[1][?7h[?12l[?25h[?25l[?7l1]) - B[1][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([0, 1]) - B[11]

[?7h[?12l[?25h[?2004l[?7h( (0) * dx, z0/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.z[0]

[?7h[?12l[?25h[?2004l[?7hz0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x^3).valuation()

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([0, 1]) - B[11][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11]

[?7h[?12l[?25h[?2004l[?7h( (x*z0) * dx, z0*z1/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[8]

[?7h[?12l[?25h[?2004l[?7h( (a*x^3*z0 + x^3*z1 + (a + 1)*x^3) * dx, z0*z1/x )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8][?7h[?12l[?25h[?25l[?7l11][?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^3).valuation()[?7h[?12l[?25h[?25l[?7lC.z[0][?7h[?12l[?25h[?25l[?7lB[11].group_action([0, 1]) - B[11][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l8][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l8].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[8].group_action([0, 1]) - B[8]

[?7h[?12l[?25h[?2004l[?7h( (x^3) * dx, z0/x )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8].group_action([0, 1]) - B[8][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l]) - B[8][?7h[?12l[?25h[?25l[?7l1]) - B[8][?7h[?12l[?25h[?25l[?7l,]) - B[8][?7h[?12l[?25h[?25l[?7l ]) - B[8][?7h[?12l[?25h[?25l[?7l0]) - B[8][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[8].group_action([1, 0]) - B[8]

[?7h[?12l[?25h[?2004l[?7h( (a*x^3) * dx, z1/x )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h>> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[ 1 * dx, 0 ,  z1 * dx, 0 ,  z0 * dx
                                                ^
User error: Identifier 'dx' has not been declared or assigned
>> /x^2 ,  x*z0 * dx, z0*z1/x^3 ]>;M := RModule(RSpace(GF(4),12), A);L := Inde
                                                                  ^
User error: Identifier 'A' has not been declared or assigned
>> 4),12), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Ge
                                          ^
User error: Identifier 'M' has not been declared or assigned
>> 4),12), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Ge
                                              ^
User error: Identifier 'L' has not been declared or assigned
>> 4),12), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Ge
                                                                ^
User error: Identifier 'L' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(C); A, B[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C); A, B[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l A, B[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(C); magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   a]
[  0   1   0]
[  0   0   1],
[  1   0   1]
[  0   1   a]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   a]
[  0   0   1],
[  1   0   0]
[  0   1   1]
[  0   0   1]
}
{
[  1 a^2   1]
[  0   1   0]
[  0   0   1],
[  1   1   1]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[8].group_action([1, 0]) - B[8][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l11][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11]

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[11][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[11]

[?7h[?12l[?25h[?2004l[?7h( (x*z0) * dx, z0*z1/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[3]

[?7h[?12l[?25h[?2004l[?7h( (x) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l A, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lA = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l2 = group_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2

[?7h[?12l[?25h[?2004l[?7h(
[    1     0     1     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     1     0     1     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     1     0]
[    0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     1],

[1 1 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 a 0]
[0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 a 0]
[0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1]
)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-3])[?7h[?12l[?25h[?25l[?7lroup_action_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[3]

[?7h[?12l[?25h[?2004l[?7h( (x) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[3][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]group_action[?7h[?12l[?25h[?25l[?7l[].group_action[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[4].group_action([1, 0]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, a + 1, 1, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[4].group_action([1, 0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([1, 0]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([1, 0]).coordinates()[?7h[?12l[?25h[?25l[?7l4].group_action([1, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 0]).cordinates()[?7h[?12l[?25h[?25l[?7l 0]).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0]).cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l,]).cordinates()[?7h[?12l[?25h[?25l[?7l ]).cordinates()[?7h[?12l[?25h[?25l[?7l1]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[4].group_action([0, 1]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[4].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l1].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[11].group_action([0, 1]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[11].group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4].group_action([0, 1]).cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[4]

[?7h[?12l[?25h[?2004l[?7h( ((a + 1)*x*z0 + x*z1) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
False
^C---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2080, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__()
   2079     # Attempt evaluation via singular.
-> 2080     coerced_x = [parent.coerce(e) for e in x]
   2081 except TypeError:

File /ext/sage/9.8/src/sage/structure/parent.pyx:1212, in sage.structure.parent.Parent.coerce()
   1211             _record_exception()
-> 1212     raise TypeError(_LazyString("no canonical coercion from %s to %s", (parent(x), self), {}))
   1213 else:

TypeError: no canonical coercion from Laurent Series Ring in t over Finite Field in a of size 2^2 to Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field in a of size 2^2

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         Traceback (most recent call last)
Cell In [1], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:48

File <string>:27, in is_M32(x)

File <string>:54, in coordinates(self, threshold, basis)

File <string>:392, in de_rham_basis(self, threshold)

File <string>:376, in lift_to_de_rham(self, fct, threshold)

File <string>:39, in expansion_at_infty(self, place)

File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.8/src/sage/structure/element.pyx:834, in sage.structure.element.Element.subs()
    832         else:
    833             variables.append(gen)
--> 834     return self(*variables)
    835 
    836 def numerical_approx(self, prec=None, digits=None, algorithm=None):

File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:449, in sage.rings.fraction_field_element.FractionFieldElement.__call__()
    447         (-2*x1*x2 + x1 + 1)/(x1 + x2)
    448     """
--> 449     return self.__numerator(*x, **kwds) / self.__denominator(*x, **kwds)
    450 
    451 def _is_atomic(self):

File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2085, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__call__()
   2083 y = parent.base_ring().zero()
   2084 for (m,c) in self.dict().iteritems():
-> 2085     y += c*mul([ x[i]**m[i] for i in m.nonzero_positions()])
   2086 return y
   2087 

File /ext/sage/9.8/src/sage/misc/misc_c.pyx:144, in sage.misc.misc_c.prod()
    142         return z
    143 
--> 144 prod = balanced_list_prod(x, 0, n, recursion_cutoff)
    145 
    146 if z is not None:

File /ext/sage/9.8/src/sage/misc/misc_c.pyx:180, in sage.misc.misc_c.balanced_list_prod()
    178     prod = <object>PySequence_Fast_GET_ITEM(L, offset)
    179     for k from offset < k < offset + count:
--> 180         prod *= <object>PySequence_Fast_GET_ITEM(L, k)
    181     return prod
    182 else:

File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
   1511 cdef int cl = classify_elements(left, right)
   1512 if HAVE_SAME_PARENT(cl):
-> 1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
   1515     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
    911 cdef LaurentSeries right = <LaurentSeries>right_r
    912 return type(self)(self._parent,
--> 913                   self.__u * right.__u,
    914                   self.__n + right.__n)
    915 

File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
   1511 cdef int cl = classify_elements(left, right)
   1512 if HAVE_SAME_PARENT(cl):
-> 1513     return (<Element>left)._mul_(right)
   1514 if BOTH_ARE_ELEMENT(cl):
   1515     return coercion_model.bin_op(left, right, mul)

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
    538 """
    539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
    541                         self.__f * (<PowerSeries_poly>right_r).__f,
    542                         prec=prec,

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
     42     ValueError: series has negative valuation
     43 """
---> 44 R = parent._poly_ring()
     45 if isinstance(f, Element):
     46     if (<Element>f)._parent is R:

File /ext/sage/9.8/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
    958         pass
    959     return False
--> 961 def _poly_ring(self):
    962     """
    963     Return the underlying polynomial ring used to represent elements of
    964     this power series ring.
   (...)
    970         Univariate Polynomial Ring in t over Integer Ring
    971     """
    972     return self.__poly_ring

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( ((a + 1)*x*z0 + x*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (a*x^5) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ),
 ( (a*x^4) * dx, z1/x^2 ),
 ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ),
 ( (0) * dx, z1/x^3 ),
 ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ),
 ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ),
 ( (x*z0) * dx, z0*z1/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[4][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1] 
 [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( ((a + 1)*x*z0 + x*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (a*x^5) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ),
 ( (a*x^4) * dx, z1/x^2 ),
 ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ),
 ( (0) * dx, z1/x^3 ),
 ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ),
 ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ),
 ( (x*z0) * dx, z0*z1/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 8, 10, 11]:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [4, 8, 10, 11]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l3]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l5]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l7]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]:

....: [?7h[?12l[?25h[?25l[?7lprint(y1, y2)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(is_M32(B[i], B))

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]:

....:     print(is_M32(B[i], B))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [7], line 2
      1 for i in [Integer(4), Integer(6), Integer(11), Integer(13), Integer(15), Integer(16), Integer(17)]:
----> 2     print(is_M32(B[i], B))

File <string>:27, in is_M32(x, B)

File <string>:60, in coordinates(self, threshold, basis)

TypeError: 'as_cech' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[4][?7h[?12l[?25h[?25l[?7l0.omega0.r().regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].coordinates(basis = B)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [8], line 1
----> 1 B[Integer(0)].coordinates(basis = B)

File <string>:60, in coordinates(self, threshold, basis)

TypeError: 'as_cech' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( ((a + 1)*x*z0 + x*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (a*x^5) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ),
 ( (a*x^4) * dx, z1/x^2 ),
 ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ),
 ( (0) * dx, z1/x^3 ),
 ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ),
 ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ),
 ( (x*z0) * dx, z0*z1/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[0]

[?7h[?12l[?25h[?2004l[?7h( (1) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0][?7h[?12l[?25h[?25l[?7l[].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].coordinates()

[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[0].coordinates(basis = B)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [12], line 1
----> 1 B[Integer(0)].coordinates(basis = B)

File <string>:60, in coordinates(self, threshold, basis)

TypeError: 'as_cech' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( ((a + 1)*x*z0 + x*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (a*x^5) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (a*x^5*z0 + x^5*z1 + (a + 1)*x^5) * dx, z0*z1/x ),
 ( (a*x^4) * dx, z1/x^2 ),
 ( (a*x^4*z0 + x^4*z1) * dx, z0*z1/x^2 ),
 ( (0) * dx, z1/x^3 ),
 ( (a*x^3*z0 + x^3*z1) * dx, z0*z1/x^3 ),
 ( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ),
 ( (x*z0) * dx, z0*z1/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]:

....:     print(is_M32(B[i], B))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lB))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(is_M32(B[i], BB))

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 6, 11, 13, 15, 16, 17]:

....:     print(is_M32(B[i], BB))

....: 

[?7h[?12l[?25h[?2004lFalse
False
True
True
True
False
False
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = a*x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l11].group_ction([0,1]).coordinates()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2

[?7h[?12l[?25h[?2004l[?7h(
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1],

[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l[0].coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l11].group_ction([0,1]).coordinates()[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[17], B[4]

[?7h[?12l[?25h[?2004l[?7h(( (x*z0) * dx, z0*z1/x^5 ), ( ((a + 1)*x*z0 + x*z1) * dx, 0 ))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[17], B[4][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[16], B[5]

[?7h[?12l[?25h[?2004l[?7h(( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ), ( (x^2) * dx, 0 ))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[16], B[5][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l6][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[16], B[6]

[?7h[?12l[?25h[?2004l[?7h(( (a*x^2*z0 + x^2*z1) * dx, z0*z1/x^4 ),
 ( ((a + 1)*x^2*z0 + x^2*z1) * dx, 0 ))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = a*x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: f0

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [24], line 1
----> 1 f0

NameError: name 'f0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf0[?7h[?12l[?25h[?25l[?7lf.valuation()\[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1

[?7h[?12l[?25h[?2004l[?7hx^7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^3).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = C.holmorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l C.holomorphic_differentials_basis()[4][?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC f0.difn()[?7h[?12l[?25h[?25l[?7l. f0.difn()[?7h[?12l[?25h[?25l[?7lz f0.difn()[?7h[?12l[?25h[?25l[?7l[ f0.difn()[?7h[?12l[?25h[?25l[?7l[] f0.difn()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0] f0.difn()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]* f0.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf0.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*f1.diffn() +C.z[0]*f0.diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [26], line 1
----> 1 om = C.z[Integer(1)]*f1.diffn() +C.z[Integer(0)]*f0.diffn()

NameError: name 'f0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*f1.diffn() +C.z[0]*f0.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l2.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*f1.diffn() +C.z[0]*f2.diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [27], line 1
----> 1 om = C.z[Integer(1)]*f1.diffn() +C.z[Integer(0)]*f2.diffn()

TypeError: unsupported operand type(s) for +: 'NoneType' and 'NoneType'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.diffn().int()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.diffn()

[?7h[?12l[?25h[?2004l[?7h(x^6) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1.diffn()[?7h[?12l[?25h[?25l[?7lom = C.z[1]*f1.diffn() +C.z[0]*f2.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l(.difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l().difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC_super.x^7)diffn() +C.z[0]*f2.diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn() +C.z[0]*f2.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la).difn()[?7h[?12l[?25h[?25l[?7l*).difn()[?7h[?12l[?25h[?25l[?7lC_super.x^7).diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l.x^7).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*(C.x^7).diffn() +C.z[0]*(a*C.x^7).diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*(C.x^7).diffn() +C.z[0]*(a*C.x^7).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation)[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.valuation()

[?7h[?12l[?25h[?2004l[?7h-22
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = a*x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: 7*2 + 1

[?7h[?12l[?25h[?2004l[?7h15
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 1 0 0]
[0 1 0 0]
[0 0 1 1]
[0 0 0 1] 
 [1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, z1/x ),
 ( (x*z0) * dx, z0*z1/x )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[0 0 1 1 0 0 0 0]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 1 0 0]
[0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 1] 
 [1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0]
[0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (x^3*z0) * dx, z0*z1/x ),
 ( (x^2) * dx, z1/x^2 ),
 ( (x^2*z0) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^3*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[16], B[6][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(eta[-2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: is_M32(eta[-1], BB)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [43], line 1
----> 1 is_M32(eta[-Integer(1)], BB)

TypeError: 'function' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(eta[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[-1], B)[?7h[?12l[?25h[?25l[?7l[-1], B)[?7h[?12l[?25h[?25l[?7l[-1], B)[?7h[?12l[?25h[?25l[?7lB[-1], B)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-1], BB)

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7lis], B)[?7h[?12l[?25h[?25l[?7li], B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2

[?7h[?12l[?25h[?2004l[?7h(
[1 0 1 0 0 0 0 0 0 0]  [1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]  [0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]  [0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]  [0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 1 0]  [0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 1 0 0]  [0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0]  [0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]  [0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]  [0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 1]
)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1A, A2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, A2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, A2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sagre
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^5

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^3*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = C.de_rhm_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOX= C.cooology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l32(B[-1], BB)[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-1], BB)

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l2], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-2], BB)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-2], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l3], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-3], BB)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-3], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l1], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[1], BB)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lsage: A1, A2 = group_action_matrices_dR(C); A1, A2

[?7h[?12l[?25h[?2004l[?7h(
[1 0 1 0 0 0 0 0 0 0]  [1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]  [0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]  [0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]  [0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 1 0]  [0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 1 0 0]  [0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0]  [0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]  [0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]  [0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 1]
)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnus()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l[16], B[6][?7h[?12l[?25h[?25l[?7l7].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[7]

[?7h[?12l[?25h[?2004l[?7h( (x^3*z0 + x*z1) * dx, z0*z1/x )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[7][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^3*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^5

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^3).valuation()[?7h[?12l[?25h[?25l[?7l^3).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x).valuation()

[?7h[?12l[?25h[?2004l[?7h-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x).valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x).diffn()

[?7h[?12l[?25h[?2004l[?7h((x^3 + z0)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[7][?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[7][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[-4]

[?7h[?12l[?25h[?2004l[?7h( (0) * dx, z0/x )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-4][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B[-4].omega8

[?7h[?12l[?25h[?2004l[?7h((x^3 + z0)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^5

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^3*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-4].omega8[?7h[?12l[?25h[?25l[?7l = Cde_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[-4]omega8[?7h[?12l[?25h[?25l[?7l-4].omega8[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B[-2].group_action([0, 1]) - B[-2]

[?7h[?12l[?25h[?2004l[?7h( (1) * dx, z0/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-2].group_action([0, 1]) - B[-2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (B[-2].group_action([0, 1]) - B[-2]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 









































 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef ch(m, M):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ldef [?7h[?12l[?25h[?25l[?7ltotal(m, M):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lreturn lhs == rhs[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lreturn[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmax(result, 0)[?7h[?12l[?25h[?25l[?7l -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lm))[?7h[?12l[?25h[?25l[?7l+))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lM))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l-))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: def te(m, M):

....:     return m - 1 - floor((m+2*M - 1)/4)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





























 [?7h[?12l[?25h[?25l[?7ltry:[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: te(3, 5)

[?7h[?12l[?25h[?2004l[?7h-1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

























 [?7h[?12l[?25h[?25l[?7lte(3, 5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: te(3, 7)

[?7h[?12l[?25h[?2004l[?7h-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





















 [?7h[?12l[?25h[?25l[?7lte(3, 7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 7)[?7h[?12l[?25h[?25l[?7l1, 7)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: te(1, 5)

[?7h[?12l[?25h[?2004l[?7h-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

















 [?7h[?12l[?25h[?25l[?7lte(1, 5)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: te(13, 17)

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 













 [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



















 [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



















 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lte(13, 17)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(13, 17)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: te(11, 13)

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 















 [?7h[?12l[?25h[?25l[?7lte(11, 13)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l9)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: te(9, 11)

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 











 [?7h[?12l[?25h[?25l[?7lte(9, 11)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l7)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l9)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: te(7,9)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor m in range(1, 20):[?7h[?12l[?25h[?25l[?7lf.valuatio()\[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/x^8

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [23], line 1
----> 1 fff = C.z[Integer(0)]*C.z[Integer(1)]/x**Integer(8)

File <string>:52, in __truediv__(self, other)

File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8[?7h[?12l[?25h[?25l[?7l./x^8[?7h[?12l[?25h[?25l[?7lCx^8[?7h[?12l[?25h[?25l[?7l.x^8[?7h[?12l[?25h[?25l[?7lx^8[?7h[?12l[?25h[?25l[?7lx^8[?7h[?12l[?25h[?25l[?7lx^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lte[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [25], line 1
----> 1 fff.coordinates()

AttributeError: 'as_function' object has no attribute 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfff.coordinates([?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9
z1^2 - z1 = x^11

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation()

[?7h[?12l[?25h[?2004l[?7h-8
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9
z1^2 - z1 = x^11

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7lOmega = C.holomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]cordinates()[?7h[?12l[?25h[?25l[?7l[].cordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BOX[1].coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^4

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation()

[?7h[?12l[?25h[?2004l[?7h-24
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^1

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^1[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation()

[?7h[?12l[?25h[?2004l[?7h-36
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff

[?7h[?12l[?25h[?2004l[?7hz0*z1/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]*C.z[1]/C.x^1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff

[?7h[?12l[?25h[?2004l[?7hz0*z1/x^8
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]^*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l2*C.z[1]/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]^/C.x^8[?7h[?12l[?25h[?25l[?7l2/C.x^8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]^2*C.z[1]^2/C.x^8

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]^2*C.z[1]^2/C.x^8[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9
z1^2 - z1 = x^11

[?2004h[?25l[?7lsage: C[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1] 
 [1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^3*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX[1].coordinates()[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOX[1].coordinates()[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l = C.chomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l= C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_M32(B[1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-1], B)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-1], BB)

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-1], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l2], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-2], BB)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-2], BB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], B)[?7h[?12l[?25h[?25l[?7l3], B)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: is_M32(B[-3], BB)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-3])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(eta[-3])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [12], line 1
----> 1 gene(eta[-Integer(3)])

TypeError: 'function' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(eta[-3])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l[-3])[?7h[?12l[?25h[?25l[?7l([-3])[?7h[?12l[?25h[?25l[?7lB[-3])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gene(B[-3])

[?7h[?12l[?25h[?2004l( (x) * dx, z0/x ) ( (x^3) * dx, z1/x )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgene(B[-3])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: gene(B[-2])

[?7h[?12l[?25h[?2004l( (1) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = C.de_rhm_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[-2]group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7lsage: B[-2].group_action([0, 1]) - B[-2]

[?7h[?12l[?25h[?2004l[?7h( (1) * dx, z0/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7l[]_[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-2].group_action([0, 1]) - B[-2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l().coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().coordinates()[?7h[?12l[?25h[?25l[?7lsage: (B[-2].group_action([0, 1]) - B[-2]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-2].group_action([0, 1]) - B[-2]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l3).cordinates()[?7h[?12l[?25h[?25l[?7l]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([0, 1]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l3].group_action([0, 1]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (B[-3].group_action([0, 1]) - B[-3]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 1, 0, 0, 1, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-3].group_action([0, 1]) - B[-3]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l1]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l,]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l ]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l0]) - B[-3]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (B[-3].group_action([1, 0]) - B[-3]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 1, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, A2 = group_action_matrices_dR(C); A1, A2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A1.kernel()

[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 0 over Finite Field of size 2
Basis matrix:
[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lind[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: I = identity_matrix(10)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1.kernel()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = A1 * C1.y[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lsage: A1 - I

[?7h[?12l[?25h[?2004l[?7h[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-3].group_action([1, 0]) - B[-3]).coordinates()[?7h[?12l[?25h[?25l[?7lA  A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV(A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l1(A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l=(A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V1 = (A1 - I).kernel()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV1 = (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - I).kernel()[?7h[?12l[?25h[?25l[?7l2 - I).kernel()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = (A2 - I).kernel()[?7h[?12l[?25h[?25l[?7l2 = (A2 - I).kernel()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V2 = (A2 - I).kernel()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV2 = (A2 - I).kernel()[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: V1.

  V1.CartesianProduct                 V1.algebra                           

  V1.Element                          V1.ambient                           

  V1.Hom                              V1.ambient_module                   >

  V1.addition_table                   V1.ambient_vector_space              

 [?7h[?12l[?25h[?25l[?7lCartesianProduct

 V1.CartesianProduct                







 <unknown> [?7h[?12l[?25h[?25l[?7lalgebra

 V1.CartesianProduct                 V1.algebra                         [?7h[?12l[?25h[?25l[?7ln_lement

 algebra         n_lement

 ambinnhilator

<ambient_modulennhilatr_basis

 mbent_vector_spacere_linearly_dependnt[?7h[?12l[?25h[?25l[?7lbas

n_lementbas      

nnhilatorbase_extend

nnhilatr_basisbase_field       

re_linearly_dependntbase_ring             [?7h[?12l[?25h[?25l[?7lis

bas      is

base_extendis_matrix

base_field       crdinality

base_ring             crtesan_product[?7h[?12l[?25h[?25l[?7lctegories

isctegories

is_matrixctegory    

crdinalityhange_rng

crtesan_productodimension      [?7h[?12l[?25h[?25l[?7loerce

ctegoriesoerce    

ctegory    oerce_embedding

hange_rngoercmap_from

odimension      mplment [?7h[?12l[?25h[?25l[?7lnstruction

oerce    nstruction

oerce_embeddingnvert_ap_from

oercmap_fromodinatemodule

mplment ordinate_ring[?7h[?12l[?25h[?25l[?7lordinae_vector

nstructionordinae_vector

nvert_ap_fromordinates     

odinatemoduledegee           

ordinate_ringdenomor    [?7h[?12l[?25h[?25l[?7ldense_module

ordinae_vectordense_module     

ordinates     dimension  

degee           irect_sum

denomor    iscrminant[?7h[?12l[?25h[?25l[?7lump

dense_module     ump        

dimension  ups    

irect_sumechlon_coordinate_vector

iscrminantechelon_coordinates[?7h[?12l[?25h[?25l[?7lechelon_form

ump        echelon_form

ups    echelon_to_user_matrix

echlon_coordinate_vectorized_basis        

echelon_coordinatesized_basis_matrix[?7h[?12l[?25h[?25l[?7llementclass

echelon_formlementclass

echelon_to_user_matrixndomrphism_ring     

ized_basis        first            

ized_basis_matrixfre_module             [?7h[?12l[?25h[?25l[?7lfre_resoution

lementclassfre_resoution

ndomrphism_ring     from_vector      

first            gen  

fre_module             gens       [?7h[?12l[?25h[?25l[?7lgensdict

fre_resoutiongensdict      

from_vector      gensdi_ecursive

gen  t_action

gens       raded_free_resolution[?7h[?12l[?25h[?25l[?7lrammatrix

gensdict      rammatrix

gensdi_ecursivehas_coerce_map_from

t_actionhasuser_basis

raded_free_resolutionhom                   [?7h[?12l[?25h[?25l[?7lindex_in

rammatrixindex_in   

has_coerce_map_fromindex_in_saturatin

hasuser_basisinject_variables

hom                   inner_product_matrix[?7h[?12l[?25h[?25l[?7ltrsection

index_in   trsection

index_in_saturatinvariat_module   

inject_variabless_ambient      

inner_product_matrixs_dense            [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: V1.intersection(V2)

[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 5 over Finite Field of size 2
Basis matrix:
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV1.intersection(V2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = (A1 - I).kernel()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W1 = (A1 - I).image()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1 = (A1 - I).image()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W2 = (A2 - I).image()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW2 = (A2 - I).image()[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W1.intersection(W2)

[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 1 over Finite Field of size 2
Basis matrix:
[0 0 0 0 0 0 0 1 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 1))[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1 - I[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l305.valuation(5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1 - I[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1, 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: A3 = matrix([[1, 1], [0, 0]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = matrix([[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: A3

[?7h[?12l[?25h[?2004l[?7h[1 1]
[0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A3.image()

[?7h[?12l[?25h[?2004l[?7hFree module of degree 2 and rank 1 over Integer Ring
Echelon basis matrix:
[1 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1.intersection(W2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = (A1 - I).image()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(A1 - I).image()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltimage()[?7h[?12l[?25h[?25l[?7lrimage()[?7h[?12l[?25h[?25l[?7laimage()[?7h[?12l[?25h[?25l[?7lnimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7lpimage()[?7h[?12l[?25h[?25l[?7loimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7leimage()[?7h[?12l[?25h[?25l[?7l(image()[?7h[?12l[?25h[?25l[?7l()image()[?7h[?12l[?25h[?25l[?7l().image()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: W1 = (A1 - I).transpose().image()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1 = (A1 - I).transpose().image()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l- I).transpose().image()[?7h[?12l[?25h[?25l[?7l- I).transpose().image()[?7h[?12l[?25h[?25l[?7l2- I).transpose().image()[?7h[?12l[?25h[?25l[?7l - I).transpose().image()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: W2 = (A2 - I).transpose().image()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW2 = (A2 - I).transpose().image()[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l.intersection(W2)[?7h[?12l[?25h[?25l[?7lintersection(W2)[?7h[?12l[?25h[?25l[?7lsage: W1.intersection(W2)

[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 1 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(B[-3].group_action([1, 0]) - B[-3]).coordinates()[?7h[?12l[?25h[?25l[?7lA  A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (A1 - I).transpose().image()

[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 4 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv3 = vector((2, 1))[?7h[?12l[?25h[?25l[?7l110[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lF10*[0])[?7h[?12l[?25h[?25l[?7lD10*[0])[?7h[?12l[?25h[?25l[?7l10*[0])[?7h[?12l[?25h[?25l[?7l10*[0])[?7h[?12l[?25h[?25l[?7lG10*[0])[?7h[?12l[?25h[?25l[?7lF10*[0])[?7h[?12l[?25h[?25l[?7l(10*[0])[?7h[?12l[?25h[?25l[?7l210*[0])[?7h[?12l[?25h[?25l[?7l()10*[0])[?7h[?12l[?25h[?25l[?7l(),10*[0])[?7h[?12l[?25h[?25l[?7l 10*[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v1 = vector(GF(2), 10*[0])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l2(2, 0))[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lvector((2, 0))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l()10*[0][?7h[?12l[?25h[?25l[?7l(10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l10*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0*[0][?7h[?12l[?25h[?25l[?7l20*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v1 = 20*[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = 20*[0][?7h[?12l[?25h[?25l[?7l2vector((2, 0))[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbase_ring(parent(x))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1 = 20*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: v = 20*[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = 20*[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l+][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: v[10+4] = 1

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[10+4] = 1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+4] = 1[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: v[10+6] = 1

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[10+6] = 1[?7h[?12l[?25h[?25l[?7lsage: v

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3.image()[?7h[?12l[?25h[?25l[?7l1 - I[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbase_ring(parent(x))[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: block_matrix([A1, A2])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [44], line 1
----> 1 block_matrix([A1, A2])

File /ext/sage/9.8/src/sage/matrix/special.py:2005, in block_matrix(*args, **kwds)
   2003 if nrows is None:
   2004     if ncols is None:
-> 2005         raise ValueError("must specify either nrows or ncols")
   2006     else:
   2007         nrows = n // ncols

ValueError: must specify either nrows or ncols
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lblock_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[A1, A2]])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: block_matrix([[A1, A2]])

[?7h[?12l[?25h[?2004l[?7h[1 0 1 0 0 0 0 0 0 0|1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0|0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1|0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 1 0|0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 1 0 0|0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0|0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0|0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0|0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lblock_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAblock_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l3block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l=block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l block_matrix([A1, A2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A1, A2]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: A3 * vector(10*[0])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [47], line 1
----> 1 A3 * vector(Integer(10)*[Integer(0)])

File /ext/sage/9.8/src/sage/structure/element.pyx:3920, in sage.structure.element.Matrix.__mul__()
   3918 
   3919         if BOTH_ARE_ELEMENT(cl):
-> 3920             return coercion_model.bin_op(left, right, mul)
   3921 
   3922         cdef long value

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Full MatrixSpace of 10 by 20 dense matrices over Finite Field of size 2' and 'Ambient free module of rank 10 over the principal ideal domain Integer Ring'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(10*[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG10*[0])[?7h[?12l[?25h[?25l[?7lF10*[0])[?7h[?12l[?25h[?25l[?7l(10*[0])[?7h[?12l[?25h[?25l[?7l210*[0])[?7h[?12l[?25h[?25l[?7l()10*[0])[?7h[?12l[?25h[?25l[?7l(),10*[0])[?7h[?12l[?25h[?25l[?7l 10*[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 * vector(GF(2), 10*[0])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [48], line 1
----> 1 A3 * vector(GF(Integer(2)), Integer(10)*[Integer(0)])

File /ext/sage/9.8/src/sage/structure/element.pyx:3920, in sage.structure.element.Matrix.__mul__()
   3918 
   3919         if BOTH_ARE_ELEMENT(cl):
-> 3920             return coercion_model.bin_op(left, right, mul)
   3921 
   3922         cdef long value

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
   1246     # We should really include the underlying error.
   1247     # This causes so much headache.
-> 1248     raise bin_op_exception(op, x, y)
   1249 
   1250 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Full MatrixSpace of 10 by 20 dense matrices over Finite Field of size 2' and 'Vector space of dimension 10 over Finite Field of size 2'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l10*[0])[?7h[?12l[?25h[?25l[?7l=block_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[], A2])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[A2])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A1], [A2]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A1], [A2]])[?7h[?12l[?25h[?25l[?7l*vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7lsage: A3 * vector(GF(2), 10*[0])

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: v

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l = 20*[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lve[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: v = vector(GF(2), v)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.image()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lght(v)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3.solve_right(v)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [53], line 1
----> 1 A3.solve_right(v)

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = vector(GF(2), v)[?7h[?12l[?25h[?25l[?7lsage: v

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lA3.solve_right(v[?7h[?12l[?25h[?25l[?7lv = vecto(GF(2), v)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 * vector(GF(2), 10*[0])[?7h[?12l[?25h[?25l[?7l=block_matrix([[A1], [A2]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l1]])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], [A1])[?7h[?12l[?25h[?25l[?7l2], [A1])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A2], [A1]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A2], [A1]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.solve_righ(v)[?7h[?12l[?25h[?25l[?7lsolve_right(v)[?7h[?12l[?25h[?25l[?7lsage: A3.solve_right(v)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [57], line 1
----> 1 A3.solve_right(v)

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3.solve_right(v)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: A3

[?7h[?12l[?25h[?2004l[?7h20 x 10 dense matrix over Finite Field of size 2 (use the '.str()' method to see the entries)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3[?7h[?12l[?25h[?25l[?7l.solve_right(v)[?7h[?12l[?25h[?25l[?7l = block_marix([[A2], [A1]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l ], [A1])[?7h[?12l[?25h[?25l[?7l-], [A1])[?7h[?12l[?25h[?25l[?7l ], [A1])[?7h[?12l[?25h[?25l[?7lI], [A1])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l_]])[?7h[?12l[?25h[?25l[?7lI]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l-]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7lI]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A3 = block_matrix([[A2 - I], [A1 - I]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A2 - I], [A1 - I]])[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.solve_righ(v)[?7h[?12l[?25h[?25l[?7lsolve_right(v)[?7h[?12l[?25h[?25l[?7lsage: A3.solve_right(v)

[?7h[?12l[?25h[?2004l[?7h(0, 1, 0, 0, 0, 0, 0, 0, 1, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef te(m, M):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
Vector space of degree 10 and dimension 1 over Finite Field of size 2
Basis matrix:
[0 0 0 0 0 0 0 1 0 0]
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [61], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:65

NameError: name 'solve_right' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), ( (x^2*z0 + z1) * dx, z0*z1/x^4 )]
Vector space of degree 16 and dimension 2 over Finite Field of size 2
Basis matrix:
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[1]

....: A3 = block_matrix([[A1 - I], [A2 - I]])

....: e = n*[0] + list(e1)

....: e = vector(GF(2), e)

....: print(A3.solve_right(e))[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[1]

....: A3 = block_matrix([[A1 - I], [A2 - I]])

....: e = n*[0] + list(e1)

....: e = vector(GF(2), e)

....: print(A3.solve_right(e))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [63], line 5
      3 e = n*[Integer(0)] + list(e1)
      4 e = vector(GF(Integer(2)), e)
----> 5 print(A3.solve_right(e))

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lthis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[0]

....: A3 = block_matrix([[A1 - I], [A2 - I]])

....: e = n*[0] + list(e1)

....: e = vector(GF(2), e)

....: print(A3.solve_right(e))[?7h[?12l[?25h[?25l[?7lsage: e1 = W.basis()[0]

....: A3 = block_matrix([[A1 - I], [A2 - I]])

....: e = n*[0] + list(e1)

....: e = vector(GF(2), e)

....: print(A3.solve_right(e))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [65], line 5
      3 e = n*[Integer(0)] + list(e1)
      4 e = vector(GF(Integer(2)), e)
----> 5 print(A3.solve_right(e))

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
Vector space of degree 10 and dimension 1 over Finite Field of size 2
Basis matrix:
[0 0 0 0 0 0 0 1 0 0]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [66], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:65

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le = vector(GF(2), e)[?7h[?12l[?25h[?25l[?7l1 = W.basis()[0][?7h[?12l[?25h[?25l[?7lsage: e1

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV1.intersection(V2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lintersection(V2)[?7h[?12l[?25h[?25l[?7lsage: V1.intersection(V2)

[?7h[?12l[?25h[?2004l[?7hVector space of degree 10 and dimension 1 over Finite Field of size 2
Basis matrix:
[0 0 0 0 0 0 0 1 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^3*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
Vector space of degree 10 and dimension 1 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0]
(0, 1, 0, 0, 0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: V1 = (A1 - I).transpose().image()

....: V2 = (A2 - I).transpose().image()

....: W1 = (A1 - I).transpose().kernel()

....: W2 = (A2 - I).transpose().kernel()

....: W = V1.intersection(V2)

....: W = W.intersection(W1)

....: W = W.intersection(W2)

....: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(GF(2), e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(GF(2), e)

....:     e3 = A3.solve_right(e)

....:     print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l....:     print(e1, e2, e3)

....: [?7h[?12l[?25h[?25l[?7lsage: V1 = (A1 - I).transpose().image()

....: V2 = (A2 - I).transpose().image()

....: W1 = (A1 - I).transpose().kernel()

....: W2 = (A2 - I).transpose().kernel()

....: W = V1.intersection(V2)

....: W = W.intersection(W1)

....: W = W.intersection(W2)

....: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(GF(2), e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(GF(2), e)

....:     e3 = A3.solve_right(e)

....:     print(e1, e2, e3)

....: 

[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 1) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), ( (x^2*z0 + z1) * dx, z0*z1/x^4 )]
(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def from_coor(coor, B):

....:     result = coor[0]*B[0]

....:     for i in range(1, len(coor)):

....:         result += coor[i]*B[i]

....:     return result[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l....:     return resut

....: [?7h[?12l[?25h[?25l[?7lsage: def from_coor(coor, B):

....:     result = coor[0]*B[0]

....:     for i in range(1, len(coor)):

....:         result += coor[i]*B[i]

....:     return resut

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[-2].group_action([0, 1]) - B[-2][?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^5) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ),
 ( (x^4) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^4 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^4 ) ( (z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x^2*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^5) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^5*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^4) * dx, z1/x^2 ),
 ( (x^4*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x^3*z0) * dx, z0*z1/x^3 ),
 ( (x^2*z0) * dx, z0*z1/x^4 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^5 ) ( (z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7lmC.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l=C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = (C.z[0]*C.z[1]/C.x^5).diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.z[0]*C.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((x^9*z0 + x^3*z1 + z0*z1)/x^6) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l = (C.z[0]*C.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l6).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: om = (C.z[0]*C.z[1]/C.x^6) * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.z[0]*C.z[1]/C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7luation[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.valuation()

[?7h[?12l[?25h[?2004l[?7h16
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.z[0]*C.z[1]/C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l= (C.z[0]*C.z[1]/C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l3) * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = (C.z[1]/C.x^3) * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation()

[?7h[?12l[?25h[?2004l[?7h10
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7l = (C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (x^3*z0 + z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^7) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^7*z0 + x*z1) * dx, z0*z1/x ),
 ( (x^6) * dx, z1/x^2 ),
 ( (x^6*z0 + z1) * dx, z0*z1/x^2 ),
 ( (x^5) * dx, z1/x^3 ),
 ( (x^5*z0) * dx, z0*z1/x^3 ),
 ( (x^4*z0) * dx, z0*z1/x^4 ),
 ( (x^3*z0) * dx, z0*z1/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ s

age
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g

it push
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git push
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g

it push
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g

it push]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^5 ) ( (x*z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, A2)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [4], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:392, in de_rham_basis(self, threshold)

File <string>:380, in lift_to_de_rham(self, fct, threshold)

ValueError: Increase threshold!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1 a^2   1]
[  0   1   0]
[  0   0   1],
[  1   1 a^2]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1   1   a]
[  0   1   0]
[  0   0   1],
[  1 a^2 a^2]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1   0   a]
[  0   1   a]
[  0   0   1],
[  1   0   0]
[  0   1   1]
[  0   0   1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^4 ) ( (x^2*z0) * dx, z0*z1/x^4 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1 a^2   a]
[  0   1   0]
[  0   0   1],
[  1   1   a]
[  0   1   0]
[  0   0   1]
}
{
[  1 a^2   1]
[  0   1   0]
[  0   0   1],
[  1   a   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   1]
[  0   0   1],
[  1   0   1]
[  0   1   1]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   1]
[  0   0   1],
[  1   0   1]
[  0   1 a^2]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   a]
[  0   0   1],
[  1   0   1]
[  0   1   1]
[  0   0   1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^4 ) ( (x^2*z0) * dx, z0*z1/x^4 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 1 0 0]
[0 1 0 0]
[0 0 1 1]
[0 0 0 1]


[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, z1/x ),
 ( (x*z0) * dx, z0*z1/x )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[0 0 1 1 0 0 0 0]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 1 0 0]
[0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 1]


[1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0]
[0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^3) * dx, z1/x ),
 ( (x^3*z0) * dx, z0*z1/x ),
 ( (x^2) * dx, z1/x^2 ),
 ( (x^2*z0) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^3 ) ( (z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^5) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ),
 ( (x^4) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^4 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [4, 6, 11, 13, 15, 16, 17]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l0]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l3]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l5]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]:

....: [?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:     print()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]:

....:     print()

....: 

[?7h[?12l[?25h[?2004l




[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]:

....: [?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7l(M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [4, 10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]:

....: [?7h[?12l[?25h[?25l[?7lprint()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7l(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:     print(is_M32(B[i], BB))

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [4, 10, 13, 14, 15]:

....:     print(is_M32(B[i], BB))

....: 

[?7h[?12l[?25h[?2004lTrue
True
True
False
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     print(e1, e2, e3)

....:     print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))[?7h[?12l[?25h[?25l[?7l....:     print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))

....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     print(e1, e2, e3)

....:     print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))

....: 

[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lspan(v1, v2)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     print(e1, e2, e3)

....:     print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l[]

()[?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li in [4, 10, 13, 14, 15]:

print(is_M32(B[], BB))

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l[]

()[?7h[?12l[?25h[?25l[?7l[]

()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lis)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lB))[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [10, 13, 14, 15]:

....:     print(gene(B[i]))

....: 

[?7h[?12l[?25h[?2004l( (x^3) * dx, z0/x ) ( (x^5) * dx, z1/x )
None
( (x^2) * dx, z0/x^2 ) ( (x^4) * dx, z1/x^2 )
None
( (0) * dx, z0/x^3 ) ( (x^3 + x^2) * dx, z1/x^3 )
None
( (1) * dx, z0/x^4 ) ( (x^2) * dx, z1/x^4 )
None
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7lfC.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7lfC.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l=C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]/C.x^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7lsage: fff.valuation()

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^4 ) ( (x*z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^2*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^5) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ),
 ( (x^4) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ),
 ( (x^2*z0 + z1) * dx, z0*z1/x^4 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^5 ) ( (x*z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [5], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:392, in de_rham_basis(self, threshold)

File <string>:380, in lift_to_de_rham(self, fct, threshold)

ValueError: Increase threshold!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 0]
[1 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
( (x^3) * dx, 0 ) ( (x^3*z1) * dx, (x*z0*z1 + z0*z1)/x^7 ) ( (x^3*z0) * dx, z0*z1/x^7 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7lsage: B\

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3*z0 + x^2*z1) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4*z0 + x^3*z1) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (x^9) * dx, z1/x ),
 ( (x^7) * dx, z0/x ),
 ( (x^9*z0 + x^8 + x^7*z1) * dx, z0*z1/x ),
 ( (x^8) * dx, z1/x^2 ),
 ( (x^6) * dx, z0/x^2 ),
 ( (x^8*z0 + x^6*z1) * dx, z0*z1/x^2 ),
 ( (x^7) * dx, z1/x^3 ),
 ( (0) * dx, z0/x^3 ),
 ( (x^7*z0 + x^5*z1) * dx, z0*z1/x^3 ),
 ( (x^4) * dx, z0/x^4 ),
 ( (x^6*z0 + x^4*z1) * dx, z0*z1/x^4 ),
 ( (x^5*z0 + x^4*z0) * dx, z0*z1/x^5 ),
 ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^6 ),
 ( (x^3*z0) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.valuation()[?7h[?12l[?25h[?25l[?7lfor i in [10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin [10, 13, 14, 15]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l7]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l0]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l9]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l4]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l5]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l2]:[?7h[?12l[?25h[?25l[?7l7]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:

....: [?7h[?12l[?25h[?25l[?7lprint(gene(B[i]))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7l(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:     print(is_M32(B[i], BB))

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:

....:     print(is_M32(B[i], BB))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [8], line 2
      1 for i in [Integer(7), Integer(10), Integer(16), Integer(19), Integer(22), Integer(24), Integer(25), Integer(26), Integer(27)]:
----> 2     print(is_M32(B[i], BB))

NameError: name 'BB' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB\[?7h[?12l[?25h[?25l[?7lOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:

....:     print(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:     print(is_M32(B[i], BB))

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:

....:     print(is_M32(B[i], BB))

....: 

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
False
True
False
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9
z1^2 - z1 = x^11

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     #print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(e1, e2, e3)

....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     print(e1, e2, e3)

....: 

[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1) (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: Z = []

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     #print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l....:     Z += [e1, e2, e3]

....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     Z += [e1, e2, e3]

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ = [][?7h[?12l[?25h[?25l[?7lsage: Z

[?7h[?12l[?25h[?2004l[?7h[(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1),
 (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
 (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1),
 (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llZ[0][?7h[?12l[?25h[?25l[?7leZ[0][?7h[?12l[?25h[?25l[?7lnZ[0][?7h[?12l[?25h[?25l[?7llen(Z[0][?7h[?12l[?25h[?25l[?7l()Z[0][?7h[?12l[?25h[?25l[?7l(Z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: len(Z[0])

[?7h[?12l[?25h[?2004l[?7h28
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV2 = (A2 - I).transpose().image()[?7h[?12l[?25h[?25l[?7l = QQ^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: V=F^28

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV=F^28[?7h[?12l[?25h[?25l[?7l.linear_dependence([v1, v3])[?7h[?12l[?25h[?25l[?7lsage: V.linear_dependence([v1, v3])

  V.CartesianProduct                 V.algebra                          V.annihilator                      V.base_extend                      V.basis_matrix                     
 

  V.Element                          V.ambient_module                   V.annihilator_basis                V.base_field                       V.cardinality                      
 

  V.Hom                              V.ambient_vector_space             V.are_linearly_dependent           V.base_ring                        V.cartesian_product                
>

  V.addition_table                   V.an_element                       V.base                             V.basis                            V.categories                       
 

 [?7h[?12l[?25h[?25l[?7lCartesianProduct

 V.CartesianProduct                







 <unknown> [?7h[?12l[?25h[?25l[?7lalgebra

 V.CartesianProduct                 V.algebra                         [?7h[?12l[?25h[?25l[?7lnnihilator

 V.algebra                          V.annihilator                     [?7h[?12l[?25h[?25l[?7lbase_extend

 V.annihilator                      V.base_extend                     [?7h[?12l[?25h[?25l[?7lis_matrix

 V.base_extend                      V.basis_matrix                    [?7h[?12l[?25h[?25l[?7lctegory

 algebra         nnihilatorbase_extendis_matrixctegory    

 ambi_modulennhilatr_basisbase_field       crdinalityhange_rng

<ambient_vector_spacere_linearly_dependntbase_ring             crtesan_productodimension      

 n_elemen    bas      isctegoriesoerce    [?7h[?12l[?25h[?25l[?7loerce_embedding

nnihilatorbase_extendis_matrixctegory    oerce_embedding

nnhilatr_basisbase_field       crdinalityhange_rngoercmap_from

re_linearly_dependntbase_ring             crtesan_productodimension      mplment 

bas      isctegoriesoerce    nstruction[?7h[?12l[?25h[?25l[?7lnvert_ap_from

base_extendis_matrixctegory    oerce_embeddingnvert_ap_from

base_field       crdinalityhange_rngoercmap_fromodinatemodule

base_ring             crtesan_productodimension      mplment ordinate_ring

isctegoriesoerce    nstructionordinae_vector[?7h[?12l[?25h[?25l[?7lordinates

is_matrixctegory    oerce_embeddingnvert_ap_fromordinates     

crdinalityhange_rngoercmap_fromodinatemoduledegee           

crtesan_productodimension      mplment ordinate_ringdenomor    

ctegoriesoerce    nstructionordinae_vectordense_module     [?7h[?12l[?25h[?25l[?7lnvert_map_from

 V.convert_map_from                 V.coordinates                     [?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l

 V.saturation                       V.span                             V.submodule_with_basis             V.sum                              V.summation_from_element_class_add

 V.save                             V.span_of_basis                    V.subspace                         V.sum_of_monomials                                                   

 V.scale                            V.sparse_module                    V.subspace_with_basis              V.sum_of_terms                                                       

 V.some_elements                    V.submodule                        V.subspaces                        V.summation                                                          [?7h[?12l[?25h[?25l[?7laturation

 V.saturation                      







 <unknown> [?7h[?12l[?25h[?25l[?7lpan

 V.saturation                       V.span                            [?7h[?12l[?25h[?25l[?7lubmodule_with_basis

 V.span                             V.submodule_with_basis            [?7h[?12l[?25h[?25l[?7lspace

 V.submodule_with_basis            

 V.subspace                        [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: V.subspace(Z)

[?7h[?12l[?25h[?2004l[?7hVector space of degree 28 and dimension 12 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lWV.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l=V.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7lV.subspace(Z)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lWV.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l=V.subspace(Z)[?7h[?12l[?25h[?25l[?7l V.subspace(Z)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: W = V.subspace(Z)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7lsage: Z[0] in W

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:

....: ....:     print(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7li])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7lj])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l=])[?7h[?12l[?25h[?25l[?7l=])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7li])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7lf])[?7h[?12l[?25h[?25l[?7lo])[?7h[?12l[?25h[?25l[?7lfor])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7lj])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7li])[?7h[?12l[?25h[?25l[?7lin])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7lr])[?7h[?12l[?25h[?25l[?7la])[?7h[?12l[?25h[?25l[?7ln])[?7h[?12l[?25h[?25l[?7lg])[?7h[?12l[?25h[?25l[?7lrange])[?7h[?12l[?25h[?25l[?7l(])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7l8])[?7h[?12l[?25h[?25l[?7l)])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7lrvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7livector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7lnvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7ltvector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7lprint(vector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7livector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7l,vector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7l vector([j = i for j in range(28)]) in W[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....: ....:     print(i, vector([j == i for j in range(28)]) in W)

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:

....: ....:     print(i, vector([j == i for j in range(28)]) in W)

....: 

[?7h[?12l[?25h[?2004l7 True
10 False
16 False
19 False
22 False
24 False
25 False
26 False
27 True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l|[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9
z1^2 - z1 = x^11

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [7, 10, 16, 19, 22, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7lff.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^7

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()\[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^11*z0 + x^9*z1 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^6

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

[?7h[?12l[?25h[?2004l[?7h(x^4*z0 + x^2*z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(Z[0])[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
( (x^3) * dx, 0 ) ( (x^3*z1) * dx, (x*z0*z1 + z0*z1)/x^7 ) ( (x^3*z0) * dx, z0*z1/x^7 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3*z0 + x^2*z1) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4*z0 + x^3*z1) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (x^9) * dx, z1/x ),
 ( (x^7) * dx, z0/x ),
 ( (x^9*z0 + x^8 + x^7*z1) * dx, z0*z1/x ),
 ( (x^8 + 1) * dx, z1/x^2 ),
 ( (0) * dx, z0/x^2 ),
 ( (x^8*z0 + x^6*z1) * dx, z0*z1/x^2 ),
 ( (x^7) * dx, z1/x^3 ),
 ( (0) * dx, z0/x^3 ),
 ( (x^7*z0 + x^5*z1) * dx, z0*z1/x^3 ),
 ( (0) * dx, z0/x^4 ),
 ( (x^6*z0 + x^4*z1) * dx, z0*z1/x^4 ),
 ( (x^5*z0 + x^4*z0) * dx, z0*z1/x^5 ),
 ( (x^4*z0 + x^3*z0) * dx, z0*z1/x^6 ),
 ( (x^3*z0) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l    [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 0]
[1 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
( (x^3) * dx, 0 ) ( (x^3*z1) * dx, z0*z1/x^6 ) ( (x^3*z0) * dx, z0*z1/x^7 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^3*z0 + x^2*z1) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^4*z0 + x^3*z0 + x^3*z1) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (x^9) * dx, z1/x ),
 ( (x^7) * dx, z0/x ),
 ( (x^9*z0 + x^8 + x^7*z1 + x^7 + x^5*z1) * dx, z0*z1/x ),
 ( (x^8 + 1) * dx, z1/x^2 ),
 ( (x^6 + x^4) * dx, z0/x^2 ),
 ( (x^8*z0 + x^6*z1 + x^4*z1 + z0) * dx, z0*z1/x^2 ),
 ( (x^7) * dx, z1/x^3 ),
 ( (0) * dx, z0/x^3 ),
 ( (x^7*z0 + x^5*z1 + x^4*z0 + x^3*z0) * dx, z0*z1/x^3 ),
 ( (0) * dx, z1/x^4 ),
 ( (x^6*z0 + x^4*z1 + x^3*z0) * dx, z0*z1/x^4 ),
 ( (x^5*z0 + x^4*z0 + x^3*z0) * dx, z0*z1/x^5 ),
 ( (x^4*z0 + x^3*z0) * dx, z0*z1/x^6 ),
 ( (x^3*z0) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')





























































 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 0]
[1 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
( (x^3) * dx, 0 ) ( (x^3*z1) * dx, z0*z1/x^6 ) ( (x^3*z0) * dx, z0*z1/x^7 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9 + x^7
z1^2 - z1 = x^11 + x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]


[1 1 0 0]
[0 1 0 0]
[0 0 1 1]
[0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^3 ) ( (z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 1 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^3 ) ( (z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 1 0 0 0 0 0 1 0 1]
[0 0 0 0 0 0 1 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, z0*z1/x^4 ) ( (z0) * dx, 0 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 0]
[1 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
( (x^3) * dx, 0 ) ( (x^3*z1) * dx, z0*z1/x^6 ) ( (x^3*z0) * dx, z0*z1/x^7 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7l= C.z[0]*C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^7

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^11*z0 + x^9*z1 + x^7*z1 + x^3*z0 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l. (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lx (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l* (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om =C.x* (C.z[1]) * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom =C.x* (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^9 + x^7
z1^2 - z1 = x^11 + x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7lx.valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation()

[?7h[?12l[?25h[?2004l[?7h26
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lon()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.z[1].valuation()

[?7h[?12l[?25h[?2004l[?7h-22
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  lo

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [48], line 1
----> 1 lo

NameError: name 'lo' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     a]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   1   0]
[  0   1   0]
[  0   0   1],
[  1   a   1]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   a]
[  0   0   1],
[  1   0   a]
[  0   1   1]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1 a^2   0]
[  0   1   0]
[  0   0   1],
[  1   1 a^2]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1 a^2]
[  0   0   1],
[  1   0   a]
[  0   1   a]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   a]
[  0   0   1],
[  1   0   a]
[  0   1   1]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   1]
[  0   0   1],
[  1   0   a]
[  0   1   0]
[  0   0   1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 )
( (x^3) * dx, 0 ) ( (x^3*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x^3*z0) * dx, z0*z1/x^5 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l= C.z[0]*C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]/C.x^5

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

[?7h[?12l[?25h[?2004l[?7h((a*x^9*z0 + x^9*z1 + z0*z1)/x^6) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l =C.x* (C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l (C.z[1]/C.x^3)* C.dx[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l) * C.dx[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l.(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lx(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l^(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l3(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l*(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.x^3*(C.z[1]) * C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.x^3*(C.z[1]) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7l.0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7laluation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation()

[?7h[?12l[?25h[?2004l[?7h-8
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[1].valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx,
 ((a + 1)*x^2*z0 + x^2*z1) * dx,
 (x^3) * dx,
 ((a + 1)*x^3*z0 + x^3*z1) * dx,
 (x^4) * dx,
 (x^5) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 0]
[1 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     #print(e1, e2, e3)

....:     print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))

....:     print(from_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8)[?7h[?12l[?25h[?25l[?7l....:     print(from_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8)

....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     #print(e1, e2, e3)

....:     print(from_coor(e1, B), from_coor(e2, B), from_coor(e3, B))

....:     print(from_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8)

....: 

[?7h[?12l[?25h[?2004l( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(1) * dx (z1) * dx (z0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^6 ) ( (x*z0) * dx, 0 )
(x) * dx (x^2*z0 + x*z1 + z1) * dx (x*z0) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, (x*z0*z1 + z0*z1)/x^6 ) ( (x^2*z0) * dx, z0*z1/x^6 )
(x^2) * dx ((x^9*z0 + x^8*z0 + x^8*z1 + x^7*z1 + x^6*z1 + z0*z1)/x^6) * dx (z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: 4416 - 3842

[?7h[?12l[?25h[?2004l[?7h574
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5+14 - 5[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: 574/12

[?7h[?12l[?25h[?2004l[?7h287/6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l574/12[?7h[?12l[?25h[?25l[?7l12.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 574/12.n()

[?7h[?12l[?25h[?2004l[?7h47.8333333333333
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = x^9

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x^2*z0 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx,
 (x^3*z0 + x^2*z1) * dx,
 (x^3) * dx,
 (x^4) * dx,
 (x^5) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ lol
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ lolsage
 ┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 0]
[1 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
(0) * dx ((x^11*z0 + x^9*z1 + z0*z1)/x^8) * dx (0) * dx
( (x^3) * dx, 0 ) ( (x^3*z1) * dx, (x*z0*z1 + z0*z1)/x^7 ) ( (x^3*z0) * dx, z0*z1/x^7 )
(0) * dx ((x^12*z0 + x^11*z0 + x^10*z1 + x^9*z1 + z0*z1)/x^8) * dx ((x^11*z0 + x^9*z1 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx,
 (x^3*z0 + x^2*z1) * dx,
 (x^2*z0) * dx,
 (x^3) * dx,
 (x^4*z0 + x^3*z1) * dx,
 (x^4) * dx,
 (x^5) * dx,
 (x^6) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.x)^(-6)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[1]/C.x^7 + C.z[0]*((C.x)^(-6) + (C.x)^(-7))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[1]/C.x^7 + C.z[0]*((C.x)^(-6) + (C.x)^(-7))[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lvaluation()\[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.valuation()

[?7h[?12l[?25h[?2004l[?7h10
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[1]/C.x^7 + C.z[0]*((C.x)^(-6) + (C.x)^(-7))[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[1]/C.x^7

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: ff.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     0     0     0     1]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1 a + 1     0     0     0     0     0     0     0     0     0     a     0]
[    0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 a 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1 a^2   a]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   a]
[  0   1   0]
[  0   0   1],
[  1   0   a]
[  0   1 a^2]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   1   a]
[  0   1   0]
[  0   0   1],
[  1   a   1]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   a]
[  0   0   1],
[  1   0   a]
[  0   1   1]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   a]
[  0   0   1],
[  1   0   0]
[  0   1 a^2]
[  0   0   1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 )
(0) * dx ((x^7*z0 + (a + 1)*x^7*z1 + (a + 1)*z0*z1)/x^6) * dx ((a*x^7*z0 + x^7*z1 + z0*z1)/x^6) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*z0*z1)/x^4 ) ( (x^2*z0) * dx, z0*z1/x^4 )
(0) * dx (x^2*z0 + (a + 1)*x^2*z1) * dx (a*x^2*z0 + x^2*z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[    1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1     0     1     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     a a + 1     1     0     0     0     0     0     0     0     0     0     a a + 1]
[    0     0     0     0     0     0     0     1     0     0     0     1     0     0     0     a     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0 a + 1     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     0     1 a + 1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     a     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1]


[    1     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     1     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0]
[    0     0     0     0 a + 1     1     1     0     0     0     0     0     0     0     0     0     1     1]
[    0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     1     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     1     0     0     0     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     1     1 a + 1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     0]
[    0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   0]
[  0   1   1]
[  0   0   1],
[  1   0   a]
[  0   1 a^2]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1   a]
[  0   0   1],
[  1   0   a]
[  0   1   0]
[  0   0   1]
}
{
[  1   0 a^2]
[  0   1 a^2]
[  0   0   1],
[  1   0   1]
[  0   1   a]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1 a^2   0]
[  0   1   0]
[  0   0   1],
[  1   0 a^2]
[  0   1   0]
[  0   0   1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, ((a + 1)*z0*z1)/x^5 ) ( (x*z0) * dx, z0*z1/x^5 )
(0) * dx ((x^7*z0 + (a + 1)*x^7*z1 + (a + 1)*x^5*z0 + (a + 1)*z0*z1)/x^6) * dx ((a*x^7*z0 + x^7*z1 + x^5*z0 + z0*z1)/x^6) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, ((a + 1)*x*z0*z1 + a*z0*z1)/x^5 ) ( (x^2*z0) * dx, (x*z0*z1 + z0*z1)/x^5 )
(0) * dx ((x^8*z0 + (a + 1)*x^8*z1 + (a + 1)*x^7*z0 + a*x^7*z1 + (a + 1)*x^6*z0 + a*x^5*z0 + a*z0*z1)/x^6) * dx ((a*x^8*z0 + x^8*z1 + a*x^7*z0 + x^7*z1 + x^6*z0 + x^5*z0 + z0*z1)/x^6) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (a*x^2*z0 + (a + 1)*x^2*z1 + x*z1) * dx,
 ((a + 1)*x^2*z0 + x^2*z1 + x*z0) * dx,
 (x^2) * dx,
 (x^3) * dx,
 (x^4) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.8/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [1], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:64, in coordinates(self, threshold, basis)

File <string>:64, in <listcomp>(.0)

File <string>:131, in serre_duality_pairing(self, fct)

File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
    583     return expression.sum(*args, **kwds)
    584 elif max(len(args),len(kwds)) <= 1:
--> 585     return sum(expression, *args, **kwds)
    586 else:
    587     from sage.symbolic.ring import SR

File <string>:131, in <genexpr>(.0)

File <string>:124, in residue(self, place)

File <string>:39, in expansion_at_infty(self, place)

File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.8/src/sage/structure/element.pyx:830, in sage.structure.element.Element.subs()
    828 if str(gen) in kwds:
    829     variables.append(kwds[str(gen)])
--> 830 elif in_dict and gen in in_dict:
    831     variables.append(in_dict[gen])
    832 else:

File /ext/sage/9.8/src/sage/structure/element.pyx:1111, in sage.structure.element.Element.__richcmp__()
   1109         return (<Element>self)._richcmp_(other, op)
   1110     else:
-> 1111         return coercion_model.richcmp(self, other, op)
   1112 
   1113 cpdef _richcmp_(left, right, int op):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
   1971 # Coerce to a common parent
   1972 try:
-> 1973     x, y = self.canonical_coercion(x, y)
   1974 except (TypeError, NotImplementedError):
   1975     pass

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1309 x_map, y_map = coercions
   1310 if x_map is not None:
-> 1311     x_elt = (<Map>x_map)._call_(x)
   1312 else:
   1313     x_elt = x

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.8/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
    636 ring_one = self.ring().one()
    637 try:
--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
    639 except (TypeError, ValueError):
    640     pass

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, z0*z1/x^6 )
(0) * dx (0) * dx ((x^8*z1 + z0)/x^4) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [3], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:392, in de_rham_basis(self, threshold)

File <string>:380, in lift_to_de_rham(self, fct, threshold)

ValueError: Increase threshold!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^8 )
(0) * dx (0) * dx ((x^6*z1 + z0)/x^2) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, 0 ) ( (x^2*z0) * dx, z0*z1/x^7 )
(0) * dx (0) * dx ((x^13*z1 + x^7*z0 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [5], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [6], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [7], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [8], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [9], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [10], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA3 = block_matrix([[A1 - I], [A2 - I]])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: C.x_series

[?7h[?12l[?25h[?2004l[?7h{0: t^-4 + t^10 + t^24 + t^26 + t^28 + t^33 + t^38 + t^49 + t^52 + t^54 + t^58 + t^61 + t^65 + t^66 + t^74 + t^77 + t^80 + t^81 + t^94 + t^100 + t^105 + t^107 + t^120 + t^123 + t^133 + t^137 + t^138 + t^145 + t^146 + t^150 + t^153 + t^154 + t^157 + t^164 + t^169 + t^171 + t^178 + t^179 + t^182 + t^185 + t^187 + t^193 + t^201 + t^206 + t^210 + t^212 + t^213 + t^225 + t^227 + t^228 + t^233 + t^235 + t^241 + t^242 + t^245 + t^249 + t^250 + t^255 + t^257 + t^268 + t^269 + t^271 + t^273 + t^274 + t^278 + t^283 + t^289 + t^292 + t^296 + t^297 + t^298 + t^299 + t^301 + t^304 + t^305 + t^306 + t^311 + t^312 + t^313 + t^325 + t^328 + t^329 + t^330 + t^332 + t^338 + t^339 + t^346 + t^347 + t^353 + t^354 + t^356 + t^357 + t^361 + t^362 + t^363 + t^367 + t^368 + t^369 + t^371 + t^377 + t^378 + t^379 + t^380 + t^385 + t^386 + t^390 + t^393 + O(t^396)}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [12], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l_series[?7h[?12l[?25h[?25l[?7lsage: C.x_series

[?7h[?12l[?25h[?2004l[?7h{0: t^-4 + t^10 + t^24 + t^26 + t^28 + t^33 + t^38 + t^49 + t^52 + t^54 + t^58 + t^61 + t^65 + t^66 + t^74 + t^77 + t^80 + t^81 + t^94 + t^100 + t^105 + t^107 + t^120 + t^123 + t^133 + t^137 + t^138 + t^145 + t^146 + t^150 + t^153 + t^154 + t^157 + t^164 + t^169 + t^171 + t^178 + t^179 + t^182 + t^185 + t^187 + t^193 + t^201 + t^206 + t^210 + t^212 + t^213 + t^225 + t^227 + t^228 + t^233 + t^235 + t^241 + t^242 + t^245 + t^249 + t^250 + t^255 + t^257 + t^268 + t^269 + t^271 + t^273 + t^274 + t^278 + t^283 + t^289 + t^292 + t^296 + t^297 + t^298 + t^299 + t^301 + t^304 + t^305 + t^306 + t^311 + t^312 + t^313 + t^325 + t^328 + t^329 + t^330 + t^332 + t^338 + t^339 + t^346 + t^347 + t^353 + t^354 + t^356 + t^357 + t^361 + t^362 + t^363 + t^367 + t^368 + t^369 + t^371 + t^377 + t^378 + t^379 + t^380 + t^385 + t^386 + t^390 + t^393 + O(t^396)}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [14], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:12

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.x_series[?7h[?12l[?25h[?25l[?7lsage: C.x_series

[?7h[?12l[?25h[?2004l[?7h{0: t^-4 + t^10 + t^24 + t^26 + t^28 + t^33 + t^38 + t^49 + t^52 + t^54 + t^58 + t^61 + t^65 + t^66 + t^74 + t^77 + t^80 + t^81 + t^94 + t^100 + t^105 + t^107 + t^120 + t^123 + t^133 + t^137 + t^138 + t^145 + t^146 + t^150 + t^153 + t^154 + t^157 + t^164 + t^169 + t^171 + t^178 + t^179 + t^182 + t^185 + t^187 + t^193 + t^201 + t^206 + t^210 + t^212 + t^213 + t^225 + t^227 + t^228 + t^233 + t^235 + t^241 + t^242 + t^245 + t^249 + t^250 + t^255 + t^257 + t^268 + t^269 + t^271 + t^273 + t^274 + t^278 + t^283 + t^289 + t^292 + t^296 + t^297 + t^298 + t^299 + t^301 + t^304 + t^305 + t^306 + t^311 + t^312 + t^313 + t^325 + t^328 + t^329 + t^330 + t^332 + t^338 + t^339 + t^346 + t^347 + t^353 + t^354 + t^356 + t^357 + t^361 + t^362 + t^363 + t^367 + t^368 + t^369 + t^371 + t^377 + t^378 + t^379 + t^380 + t^385 + t^386 + t^390 + t^393 + O(t^396)}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: C.prec

[?7h[?12l[?25h[?2004l[?7h700
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 )
(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 )
(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 )
(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     #print(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(e1, e2, e3)

....: [?7h[?12l[?25h[?25l[?7lsage: for e1 in W.basis():

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)

....:     e = vector(F, e)

....:     e2 = A3.solve_right(e)

....:     e = list(e1) + n*[0]

....:     e = vector(F, e)

....:     e3 = A3.solve_right(e)

....:     print(e1, e2, e3)

....: 

[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.prec[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.valuation()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z1) * dx, 0 ),
 ( (x^5*z1 + x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^2*z1) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^3*z1) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^4*z1) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (x^11) * dx, z0/x ),
 ( (x^11*z1 + x^7 + x^3*z0) * dx, z0*z1/x ),
 ( (x^2) * dx, z1/x^2 ),
 ( (x^10) * dx, z0/x^2 ),
 ( (x^10*z1 + x^2*z0) * dx, z0*z1/x^2 ),
 ( (x^9) * dx, z0/x^3 ),
 ( (x^9*z1 + x^5*z1) * dx, z0*z1/x^3 ),
 ( (x^8) * dx, z0/x^4 ),
 ( (x^8*z1 + z0) * dx, z0*z1/x^4 ),
 ( (x^7) * dx, z0/x^5 ),
 ( (x^7*z1) * dx, z0*z1/x^5 ),
 ( (x^6*z1) * dx, z0*z1/x^6 ),
 ( (x^5*z1) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l e1 in W.basis():[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e1 in W.basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li in [7, 10, 16, 19, 22, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin [7, 10, 16, 19, 22, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l5 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l, 16, 19, 2, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l1, 24, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l3, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....: [?7h[?12l[?25h[?25l[?7lprint(e1, e2, e3)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lis_M3(B[i], BB))[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7l(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l....:     print(is_M32(B[i], BB))

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....:     print(is_M32(B[i], BB))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [8], line 2
      1 for i in [Integer(5), Integer(16), Integer(19), Integer(21), Integer(23), Integer(25), Integer(26), Integer(27)]:
----> 2     print(is_M32(B[i], BB))

File <string>:27, in is_M32(x, B)

File <string>:54, in coordinates(self, threshold, basis)

File <string>:392, in de_rham_basis(self, threshold)

File <string>:380, in lift_to_de_rham(self, fct, threshold)

ValueError: Increase threshold!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     n = len(x.coordinates(basis = B, threshold = 20))

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     y1_coor = y1.coordinates(basis = B, threshold = 20)

....:     if y1_coor == vector(n*[0]):

....:         return False

....:     if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     y2_coor = y2.coordinates()

....:     if y2_coor == vector(n*[0]):

....:         return False

....:     if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

....:         return False

....:     return True[?7h[?12l[?25h[?25l[?7lFx.curve.base_ring

y1 = x - x.groupaction([0, 1])

_coor = y1.coordinates(basis = B, threshold = 20)

if y1_coor == vector(n*[0]):

   returnFalse

if(y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

([1, 0]) - y1).coordnates(basis = B, threshold = 20) != vector(n*[0]):

       return False

y2= x - x.group_action([1, 0])

_coor = y2.coordinates()

if y2_coor == vector(n*[0]):

   returnFalse

if(y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

([1, 0]) - y2).coordnates(basis = B, threshold = 20) != vector(n*[0]):

       return False

V=F^n

if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

   return False

retun True

[?7h[?12l[?25h[?25l[?7l....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     y1_coor = y1.coordinates(basis = B, threshold = 20)

....:     if y1_coor == vector(n*[0]):

....:         return False

....:     if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     y2_coor = y2.coordinates()

....:     if y2_coor == vector(n*[0]):

....:         return False

....:     if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

....:         return False

....:     return True

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     n = len(x.coordinates(basis = B, threshold = 20))

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     y1_coor = y1.coordinates(basis = B, threshold = 20)

....:     if y1_coor == vector(n*[0]):

....:         return False

....:     if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     y2_coor = y2.coordinates()

....:     if y2_coor == vector(n*[0]):

....:         return False

....:     if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

....:         return False

....:     return True[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: defis_M32(x, B):

nlen(x.coordinates(basis = B, threshold = 20))

F = x.curve.basering

 = x - x.group_action([0, 1])

y1_coor = y1.coordinates(basis = B, threshold = 20)

ify1_coor== vector(n*[0]):

   return False

    if (y1.group_acton([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

([1,0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

   return False

 = x - x.group_action([1, 0])

y2_coor = y2.coordinates()

ify2_coor== vector(n*[0]):

   return False

    if (y2.group_acton([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

([1,0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

  return False

V = F^n

iflen(V.linear_dependence([y1_coor, y2_coor])) > 0:

    eturn False[?7h[?12l[?25h[?25l[?7lfori in [5, 16, 19, 21, 23, 25, 26, 27]:

print(is_M32(B[], BB))

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....:     print(is_M32(B[i], BB))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [10], line 2
      1 for i in [Integer(5), Integer(16), Integer(19), Integer(21), Integer(23), Integer(25), Integer(26), Integer(27)]:
----> 2     print(is_M32(B[i], BB))

Cell In [9], line 11, in is_M32(x, B)
      9     return False
     10 y2 = x - x.group_action([Integer(1), Integer(0)])
---> 11 y2_coor = y2.coordinates()
     12 if y2_coor == vector(n*[Integer(0)]):
     13     return False

File <string>:54, in coordinates(self, threshold, basis)

File <string>:392, in de_rham_basis(self, threshold)

File <string>:380, in lift_to_de_rham(self, fct, threshold)

ValueError: Increase threshold!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     n = len(x.coordinates(basis = B, threshold = 20))

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     y1_coor = y1.coordinates(basis = B, threshold = 20)

....:     if y1_coor == vector(n*[0]):

....:         return False

....:     if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     y2_coor = y2.coordinates(basis = B, threshold = 20)

....:     if y2_coor == vector(n*[0]):

....:         return False

....:     if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

....:         return False

....:     return True[?7h[?12l[?25h[?25l[?7lFx.curve.base_ring

y1 = x - x.groupaction([0, 1])

_coor = y1.coordinates(basis = B, threshold = 20)

if y1_coor == vector(n*[0]):

   returnFalse

if(y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

([1, 0]) - y1).coordnates(basis = B, threshold = 20) != vector(n*[0]):

       return False

y2= x - x.group_action([1, 0])

_coor = y2.coordinates(basis = B, threshold = 20)

if y2_coor == vector(n*[0]):

   returnFalse

if(y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

([1, 0]) - y2).coordnates(basis = B, threshold = 20) != vector(n*[0]):

       return False

V=F^n

if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

   return False

retun True

[?7h[?12l[?25h[?25l[?7l....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     y1_coor = y1.coordinates(basis = B, threshold = 20)

....:     if y1_coor == vector(n*[0]):

....:         return False

....:     if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     y2_coor = y2.coordinates(basis = B, threshold = 20)

....:     if y2_coor == vector(n*[0]):

....:         return False

....:     if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

....:         return False

....:     return True

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     n = len(x.coordinates(basis = B, threshold = 20))

....:     F = x.curve.base_ring

....:     y1 = x - x.group_action([0, 1])

....:     y1_coor = y1.coordinates(basis = B, threshold = 20)

....:     if y1_coor == vector(n*[0]):

....:         return False

....:     if (y1.group_action([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

....: ([1, 0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     y2 = x - x.group_action([1, 0])

....:     y2_coor = y2.coordinates(basis = B, threshold = 20)

....:     if y2_coor == vector(n*[0]):

....:         return False

....:     if (y2.group_action([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

....: ([1, 0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

....:         return False

....:     V = F^n

....:     if len(V.linear_dependence([y1_coor, y2_coor])) > 0:

....:         return False

....:     return True[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: defis_M32(x, B):

nlen(x.coordinates(basis = B, threshold = 20))

F = x.curve.basering

 = x - x.group_action([0, 1])

y1_coor = y1.coordinates(basis = B, threshold = 20)

ify1_coor== vector(n*[0]):

   return False

    if (y1.group_acton([0, 1]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y1.group_actio
n

([1,0]) - y1).coordinates(basis = B, threshold = 20) != vector(n*[0]):

   return False

 = x - x.group_action([1, 0])

y2_coor = y2.coordinates(basis = B, threshold = 20)

ify2_coor== vector(n*[0]):

   return False

    if (y2.group_acton([0, 1]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]) or (y2.group_actio
n

([1,0]) - y2).coordinates(basis = B, threshold = 20) != vector(n*[0]):

  return False

V = F^n

iflen(V.linear_dependence([y1_coor, y2_coor])) > 0:

    eturn False[?7h[?12l[?25h[?25l[?7lfori in [5, 16, 19, 21, 23, 25, 26, 27]:

print(is_M32(B[], BB))

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....:     print(is_M32(B[i], BB))

....: 

[?7h[?12l[?25h[?2004lTrue
True
True
False
True
False
False
False
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 















 [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^13
z1^2 - z1 = x^5

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, 0 ) ( (x*z0) * dx, z0*z1/x^7 )
(0) * dx (0) * dx ((x^13*z1 + x^5*z0 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....:     print(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg0 = omega.int()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l....:     gene(B[i])

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....:     gene(B[i])

....: 

[?7h[?12l[?25h[?2004l( (x^5) * dx, 0 ) ( (x) * dx, 0 )
( (x^11) * dx, z0/x ) ( (x^3) * dx, z1/x )
( (x^10) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 )
( (x^9 + x^5) * dx, z0/x^3 ) ( (0) * dx, z1/x^3 )
( (x^8) * dx, z0/x^4 ) ( (1) * dx, z1/x^4 )
( (x^7) * dx, z0/x^5 ) ( (0) * dx, z1/x^5 )
( (x^6) * dx, z0/x^6 ) ( (0) * dx, z1/x^6 )
( (x^5) * dx, z0/x^7 ) ( (0) * dx, z1/x^7 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....:     gene(B[i])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l6]:[?7h[?12l[?25h[?25l[?7l,]:[?7h[?12l[?25h[?25l[?7l ]:[?7h[?12l[?25h[?25l[?7l1]:[?7h[?12l[?25h[?25l[?7l9]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l....:     gene(B[i])

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [16, 19]:

....:     gene(B[i])

....: 

[?7h[?12l[?25h[?2004l( (x^11) * dx, z0/x ) ( (x^3) * dx, z1/x )
( (x^10) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z1) * dx, 0 ),
 ( (x^5*z1 + x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^2*z1) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^3*z1) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^4*z1) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (x^11) * dx, z0/x ),
 ( (x^11*z1 + x^7 + x^3*z0) * dx, z0*z1/x ),
 ( (x^2) * dx, z1/x^2 ),
 ( (x^10) * dx, z0/x^2 ),
 ( (x^10*z1 + x^2*z0) * dx, z0*z1/x^2 ),
 ( (x^9) * dx, z0/x^3 ),
 ( (x^9*z1 + x^5*z1) * dx, z0*z1/x^3 ),
 ( (x^8) * dx, z0/x^4 ),
 ( (x^8*z1 + z0) * dx, z0*z1/x^4 ),
 ( (x^7) * dx, z0/x^5 ),
 ( (x^7*z1) * dx, z0*z1/x^5 ),
 ( (x^6*z1) * dx, z0*z1/x^6 ),
 ( (x^5*z1) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^13
z1^2 - z1 = x^5

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[1].valuton()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]/C.x).coordinates()

[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]/C.x).cordinates()[?7h[?12l[?25h[?25l[?7l0]/C.x).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x).coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).cordinates()[?7h[?12l[?25h[?25l[?7l5).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]/C.x^5).coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]/C.x^5).coordinates()[?7h[?12l[?25h[?25l[?7l).coordinates()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: for i in [16, 19]:

....:     gene(B[i])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l5, 16, 19, 21, 23, 25, 26, 27]:

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l....:     gene(B[i])

....: [?7h[?12l[?25h[?25l[?7lsage: for i in [5, 16, 19, 21, 23, 25, 26, 27]:

....:     gene(B[i])

....: 

[?7h[?12l[?25h[?2004l( (x^5) * dx, 0 ) ( (x) * dx, 0 )
( (x^11) * dx, z0/x ) ( (x^3) * dx, z1/x )
( (x^10) * dx, z0/x^2 ) ( (x^2) * dx, z1/x^2 )
( (x^9 + x^5) * dx, z0/x^3 ) ( (0) * dx, z1/x^3 )
( (x^8) * dx, z0/x^4 ) ( (1) * dx, z1/x^4 )
( (x^7) * dx, z0/x^5 ) ( (0) * dx, z1/x^5 )
( (x^6) * dx, z0/x^6 ) ( (0) * dx, z1/x^6 )
( (x^5) * dx, z0/x^7 ) ( (0) * dx, z1/x^7 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: lo

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [10], line 1
----> 1 lo

NameError: name 'lo' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^7 ) ( (x*z0) * dx, 0 )
(0) * dx ((x^13*z0 + x^5*z1 + z0*z1)/x^8) * dx (0) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW = V.subspace(Z)[?7h[?12l[?25h[?25l[?7l1 = (A1 - I).transpose().kernel()[?7h[?12l[?25h[?25l[?7l.intersection(W2)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrsection(W2)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lV)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: W1.intersection(W2).intersection(V1).basis()

[?7h[?12l[?25h[?2004l[?7h[
(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^5*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^3*z0) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^4*z0) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (x^11) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ),
 ( (x^10) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^9) * dx, z1/x^3 ),
 ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ),
 ( (x^8) * dx, z1/x^4 ),
 ( (x^8*z0 + z1) * dx, z0*z1/x^4 ),
 ( (x^7) * dx, z1/x^5 ),
 ( (x^7*z0) * dx, z0*z1/x^5 ),
 ( (x^6*z0) * dx, z0*z1/x^6 ),
 ( (x^5*z0) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in [5, 16, 19, 21, 23, 25, 26, 27]:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le1 in W.basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lW1.intersection(W2).intersection(V1).basis()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis():

....: [?7h[?12l[?25h[?25l[?7lprint(is_M32(B[i], BB))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lfrom_coor(e1, B).omega8, from_coor(e2, B).omega8, from_coor(e3, B).omega8)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(from_coor(e, B))

....: [?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis():

....:     print(from_coor(e, B))

....: 

[?7h[?12l[?25h[?2004l( (1) * dx, 0 )
( (x) * dx, 0 )
( (x^2) * dx, 0 )
( (x^3) * dx, 0 )
( (x^4) * dx, 0 )
( (x^5) * dx, 0 )
( (x^6 + x^2) * dx, z0/x^2 )
( (x^11) * dx, z1/x )
( (x^10) * dx, z1/x^2 )
( (x^9) * dx, z1/x^3 )
( (x^8) * dx, z1/x^4 )
( (x^7) * dx, z1/x^5 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e in W1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for e in B:

....: [?7h[?12l[?25h[?25l[?7lif len(V.linear_dependence([y1_coor, y2_coor])) > 0:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l32[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: BOX = C.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lOM - de_rham_witt_lift_form0(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e in B:

....: ....:     if is_M32(e, B[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l     if is_M32(e, BB):

 [?7h[?12l[?25h[?25l[?7l if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l: if is_M32(e, B):[?7h[?12l[?25h[?25l[?7l

....:          if is_M32(e, BB):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:          if is_M32(e, BB):

....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:              print(gene(e))

....: [?7h[?12l[?25h[?25l[?7lsage: for e in B:

....:          if is_M32(e, BB):

....:              print(gene(e))

....: 

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [18], line 2
      1 for e in B:
----> 2          if is_M32(e, BB):
      3              print(gene(e))

File <string>:33, in is_M32(x, B)

File <string>:61, in coordinates(self, threshold, basis)

File <string>:61, in <listcomp>(.0)

File <string>:131, in serre_duality_pairing(self, fct)

File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
    583     return expression.sum(*args, **kwds)
    584 elif max(len(args),len(kwds)) <= 1:
--> 585     return sum(expression, *args, **kwds)
    586 else:
    587     from sage.symbolic.ring import SR

File <string>:131, in <genexpr>(.0)

File <string>:124, in residue(self, place)

File <string>:39, in expansion_at_infty(self, place)

File /ext/sage/9.8/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.8/src/sage/structure/element.pyx:830, in sage.structure.element.Element.subs()
    828 if str(gen) in kwds:
    829     variables.append(kwds[str(gen)])
--> 830 elif in_dict and gen in in_dict:
    831     variables.append(in_dict[gen])
    832 else:

File /ext/sage/9.8/src/sage/structure/element.pyx:1111, in sage.structure.element.Element.__richcmp__()
   1109         return (<Element>self)._richcmp_(other, op)
   1110     else:
-> 1111         return coercion_model.richcmp(self, other, op)
   1112 
   1113 cpdef _richcmp_(left, right, int op):

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
   1971 # Coerce to a common parent
   1972 try:
-> 1973     x, y = self.canonical_coercion(x, y)
   1974 except (TypeError, NotImplementedError):
   1975     pass

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
   1309 x_map, y_map = coercions
   1310 if x_map is not None:
-> 1311     x_elt = (<Map>x_map)._call_(x)
   1312 else:
   1313     x_elt = x

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /ext/sage/9.8/src/sage/rings/fraction_field.py:534, in FractionField_generic._element_constructor_(self, x, y, coerce)
    522     """
    523     Return if ``self`` is exact which is if the underlying ring is exact.
    524 
   (...)
    530         False
    531     """
    532     return self.ring().is_exact()
--> 534 def _element_constructor_(self, x, y=None, coerce=True):
    535     """
    536     Construct an element of this fraction field.
    537 
   (...)
    629         -1/2/(a^2 + a)
    630     """
    631     if isinstance(x, (list, tuple)) and len(x) == 1:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e in B:

....:          if is_M32(e, BB):

....:              print(gene(e))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7legene(e)[?7h[?12l[?25h[?25l[?7l,gene(e)[?7h[?12l[?25h[?25l[?7l gene(e)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:              print(e, gene(e))

....: [?7h[?12l[?25h[?25l[?7lsage: for e in B:

....:          if is_M32(e, BB):

....:              print(e, gene(e))

....: 

[?7h[?12l[?25h[?2004l( (x) * dx, 0 ) ( (x^5) * dx, 0 )
( (x^5*z0 + x*z1) * dx, 0 ) None
( (x^3) * dx, z0/x ) ( (x^11) * dx, z1/x )
( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ) None
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [19], line 2
      1 for e in B:
----> 2          if is_M32(e, BB):
      3              print(e, gene(e))

File <string>:27, in is_M32(x, B)

File <string>:91, in coordinates(self, threshold, basis)

File <string>:92, in coordinates(self, basis)

File <string>:139, in holomorphic_differentials_basis(self, threshold)

File <string>:425, in holomorphic_combinations(S)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:75, in __rmul__(self, constant)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def gene(x):

....:     y1 = x - x.group_action([0, 1])

....:     y2 = x - x.group_action([1, 0])

....:     return(y1, y2)[?7h[?12l[?25h[?25l[?7l....:     return(y1, y2)

....: [?7h[?12l[?25h[?25l[?7lsage: def gene(x):

....:     y1 = x - x.group_action([0, 1])

....:     y2 = x - x.group_action([1, 0])

....:     return(y1, y2)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def gene(x):

....:     y1 = x - x.group_action([0, 1])

....:     y2 = x - x.group_action([1, 0])

....:     return(y1, y2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfore in B:

   if is_M32(e, BB):

     print(e, gene(e))

 [?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for e in B:

....:          if is_M32(e, BB):

....:              print(e, gene(e))

....: 

[?7h[?12l[?25h[?2004l( (x^5*z0 + x*z1) * dx, 0 ) (( (x) * dx, 0 ), ( (x^5) * dx, 0 ))
( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ) (( (x^3) * dx, z0/x ), ( (x^11) * dx, z1/x ))
( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ) (( (x^2) * dx, z0/x^2 ), ( (x^10) * dx, z1/x^2 ))
( (x^8*z0 + z1) * dx, z0*z1/x^4 ) (( (1) * dx, z0/x^4 ), ( (x^8) * dx, z1/x^4 ))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e in B:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lW1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7l1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis():

....: [?7h[?12l[?25h[?25l[?7lprint(from_coor(e, B))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(from_coor(e, B))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l(from_coor(e, B))[?7h[?12l[?25h[?25l[?7l....:     print(from_coor(e, B))

....: [?7h[?12l[?25h[?25l[?7l....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = n*[0] + list(e1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7l[]list(e1)[?7h[?12l[?25h[?25l[?7l[list(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7llist(e1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

print(fromcoo(e, B))

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = list(e) +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l....:     e = list(e) + n*[0]

....: [?7h[?12l[?25h[?25l[?7le3 = A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l = vector(F, e)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lvector(F, e)[?7h[?12l[?25h[?25l[?7l....:     e = vector(F, e)

....: [?7h[?12l[?25h[?25l[?7lprint(from_coor(e, B))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()r[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print('e2', A3.solve_right(e))

....: [?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis():

....:     n = len(list(e))

....:     print(from_coor(e, B))

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = list(e) + n*[0]

....:     e = vector(F, e)

....:     print('e2', A3.solve_right(e))

....: 

[?7h[?12l[?25h[?2004l( (1) * dx, 0 )
e2 (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 )
e2 (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 )
e2 (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^3) * dx, 0 )
e2 (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^4) * dx, 0 )
e2 (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^5) * dx, 0 )
e2 (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
( (x^6 + x^2) * dx, z0/x^2 )
e2 (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
( (x^11) * dx, z1/x )
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [22], line 7
      5 e = list(e) + n*[Integer(0)]
      6 e = vector(F, e)
----> 7 print('e2', A3.solve_right(e))

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis():

....:     n = len(list(e))

....:     print(from_coor(e, B))

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = list(e) + n*[0]

....:     e = vector(F, e)

....:     print('e2', A3.solve_right(e))[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()

....: 

....:     print('e2', A3.solve_right(e))[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l print('e2', A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfA3.solve_right(e)[?7h[?12l[?25h[?25l[?7lrA3.solve_right(e)[?7h[?12l[?25h[?25l[?7loA3.solve_right(e)[?7h[?12l[?25h[?25l[?7lmA3.solve_right(e)[?7h[?12l[?25h[?25l[?7l_A3.solve_right(e)[?7h[?12l[?25h[?25l[?7lcA3.solve_right(e)[?7h[?12l[?25h[?25l[?7loA3.solve_right(e)[?7h[?12l[?25h[?25l[?7loA3.solve_right(e)[?7h[?12l[?25h[?25l[?7lrA3.solve_right(e)[?7h[?12l[?25h[?25l[?7l(A3.solve_right(e)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:         print('e2', from_coor(A3.solve_right(e), B))

....: [?7h[?12l[?25h[?25l[?7l....: 

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le = vector(F, e)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lexcept[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lpass[?7h[?12l[?25h[?25l[?7l....:         pass

....: [?7h[?12l[?25h[?25l[?7lsage: for e in W1.intersection(W2).intersection(V1).basis():

....:     n = len(list(e))

....:     print(from_coor(e, B))

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = list(e) + n*[0]

....:     e = vector(F, e)

....:     try:

....:         print('e2', from_coor(A3.solve_right(e), B))

....:     except:

....:         pass

....: 

[?7h[?12l[?25h[?2004l( (1) * dx, 0 )
e2 ( (z0) * dx, 0 )
( (x) * dx, 0 )
e2 ( (x*z0) * dx, 0 )
( (x^2) * dx, 0 )
e2 ( (x^2*z0) * dx, 0 )
( (x^3) * dx, 0 )
e2 ( (x^3*z0) * dx, 0 )
( (x^4) * dx, 0 )
e2 ( (x^4*z0) * dx, 0 )
( (x^5) * dx, 0 )
e2 ( (x^5*z0) * dx, z0*z1/x^7 )
( (x^6 + x^2) * dx, z0/x^2 )
e2 ( (x^6*z0 + x^2*z0) * dx, z0*z1/x^6 )
( (x^11) * dx, z1/x )
( (x^10) * dx, z1/x^2 )
( (x^9) * dx, z1/x^3 )
e2 ( (x^9*z0) * dx, (x^4*z0*z1 + z0*z1)/x^7 )
( (x^8) * dx, z1/x^4 )
e2 ( (x^8*z0) * dx, z0*z1/x^4 )
( (x^7) * dx, z1/x^5 )
e2 ( (x^7*z0) * dx, z0*z1/x^5 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^5*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^3*z0) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^4*z0) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (x^11) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ),
 ( (x^10) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^9) * dx, z1/x^3 ),
 ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ),
 ( (x^8) * dx, z1/x^4 ),
 ( (x^8*z0 + z1) * dx, z0*z1/x^4 ),
 ( (x^7) * dx, z1/x^5 ),
 ( (x^7*z0) * dx, z0*z1/x^5 ),
 ( (x^6*z0) * dx, z0*z1/x^6 ),
 ( (x^5*z0) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^5
z1^2 - z1 = x^13

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[1].valuton()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]*C.x*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]*C.x*C.dx).valuation()

[?7h[?12l[?25h[?2004l[?7h-4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.divides(x^2)[?7h[?12l[?25h[?25l[?7li.omega0.r()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^*C.dx,[?7h[?12l[?25h[?25l[?7l8*C.dx,[?7h[?12l[?25h[?25l[?7l*C.dx,[?7h[?12l[?25h[?25l[?7l9*C.dx,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.omega0.r()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates(basis = B, threshold = 20)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [28], line 1
----> 1 xi.coordinates(basis = B, threshold = Integer(20))

TypeError: superelliptic_cech.coordinates() got an unexpected keyword argument 'basis'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates(basis = B, threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7lthreshold = 20)[?7h[?12l[?25h[?25l[?7l(threshold = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.valuation()

[?7h[?12l[?25h[?2004l[?7h-36
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.valuation()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

[?7h[?12l[?25h[?2004l[?7h((x^9*z1) * dx, (x^4*z0*z1 + z0*z1)/x^7, ((x^17*z0 + x^17*z1 + x^13*z0 + x^9*z1 + x^5*z1 + x^4*z0*z1 + z0*z1)/x^8) * dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7l.omega8.valuation()[?7h[?12l[?25h[?25l[?7lcoordinates(basis = B, threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, C.z[0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, C.z[0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8.valuation()[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.valuation()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.valuation()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: xi.omega8

[?7h[?12l[?25h[?2004l[?7h((x^13*z0 + x^9*z1 + x^5*z1 + x^4*z0*z1 + z0*z1)/x^8) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lz[1].valuton()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]/C.x^3*C.dx).valuation()

[?7h[?12l[?25h[?2004l[?7h12
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x^5*z0 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx,
 (x^2*z0) * dx,
 (x^3) * dx,
 (x^3*z0) * dx,
 (x^4) * dx,
 (x^4*z0) * dx,
 (x^5) * dx,
 (x^6) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7lx.<x> = PolynomialRing(F[?7h[?12l[?25h[?25l[?7l.<x> = PolynomialRing(F)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rx.<x> = PolynomialRing(GF(2))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor e in W1.intersection(W2).intersection(V1).basis():[?7h[?12l[?25h[?25l[?7l =x^3 + x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lsage: f = x^6

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^6[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.nth_root(2)

[?7h[?12l[?25h[?2004l[?7hx^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^7 ) ( (x*z0) * dx, 0 )
(0) * dx ((x^13*z0 + x^5*z1 + z0*z1)/x^8) * dx (0) * dx
---------------------------------------------------------
AttributeError          Traceback (most recent call last)
Cell In [4], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:87

File <string>:83, in alpha(C)

AttributeError: 'as_cover' object has no attribute 'list_of_functions'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

  C.a_number                            C.branch_points                       C.de_rham_basis                       
 

  C.at_most_poles                       C.cartier_matrix                      C.dx                                  
 

  C.at_most_poles_forms                 C.characteristic                      C.dx_series                           
>

  C.base_ring                           C.cohomology_of_structure_sheaf_basis C.exponent_of_different               
 

 [?7h[?12l[?25h[?25l[?7la_number

 C.a_number                           







 <unknown> [?7h[?12l[?25h[?25l[?7lbranch_points

 C.a_number                            C.branch_points                      [?7h[?12l[?25h[?25l[?7lde_rham_basi

 C.branch_points                       C.de_rham_basis                      [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim

 branch_pointsde_rham_basiexponent_of_different_prim

 cartiermatrixdx            fct_field

<characeristic     dx_seris     function

 cohomoloy_of_structure_sheaf_basisexpnent_of_different              genus                [?7h[?12l[?25h[?25l[?7lgroup

de_rham_basiexponent_of_different_primgroup                     

dx            fct_fieldheight   

dx_seris     functionholomorphic_differentials_basis

expnent_of_different              genus                ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps

exponent_of_different_primgroup                     jumps

fct_fieldheight   lift_o_de_rham

functionholomorphic_differentials_basismagical_element                

genus                ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lone

group                     jumpsone  

height   lift_o_de_rhamprec           

holomorphic_differentials_basismagical_element                pseudo_magical_element

ith_ramification_gpnb_of_pts_at_nfty quotien          [?7h[?12l[?25h[?25l[?7lramification_jumps

jumpsone  ramification_jumps

lift_o_de_rhamprec           uniformizer

magical_element                pseudo_magical_elementx                     

nb_of_pts_at_nfty quotien          x_series[?7h[?12l[?25h[?25l[?7ly

one  ramification_jumpsy                  

prec           uniformizery_series    

pseudo_magical_elementx                     z 

quotien          x_seriesz 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lramification_jumps

 C.ramification_jumps                  C.y                                  [?7h[?12l[?25h[?25l[?7lone

 C.one                                 C.ramification_jumps                 [?7h[?12l[?25h[?25l[?7ljumps

jumpsone               ramification_jumps 

lift_to_de_rhamprec       uniformizer 

magical_element       pseudo_magical_elementx>

nb_of_ps_at_inftyquotientx 
[?7h[?12l[?25h[?25l[?7lgroup

groupjumpsone               

heigh         lift_to_de_rhamprec       

holomorphic_differentials_basismagical_element       pseudo_magical_element

ith_ramificaton_gpnb_of_ps_at_inftyquotient[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim

exponent_of_different_primgroupjumps

fct_fieldheigh         lift_to_de_rham

functions                      holomorphic_differentials_basismagical_element       

genus              ith_ramificaton_gpnb_of_ps_at_infty[?7h[?12l[?25h[?25l[?7lde_rham_basis

de_rham_basis             exponent_of_different_primgroup

dx       fct_fieldheigh         

dx_seriefunctions                      holomorphic_differentials_basis

exponent_of_differentgenus              ith_ramificaton_gp[?7h[?12l[?25h[?25l[?7lbranch_point

branch_pointde_rham_basis             exponent_of_different_prim

cartier_matrixdx       fct_field

charactristicdx_seriefunctions                      

cohmology_of_structure_sheaf_basisexponent_of_differentgenus              [?7h[?12l[?25h[?25l[?7la_number

 a_number     branch_pointde_rham_basis             

 at_mostpoles cartier_matrixdx       

 at_mos_poles_formscharactristicdx_serie

 base_rin                          cohmology_of_structure_sheaf_basisexponent_of_different[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^7 ) ( (x*z0) * dx, 0 )
(0) * dx ((x^13*z0 + x^5*z1 + z0*z1)/x^8) * dx (0) * dx
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [5], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:87

File <string>:85, in alpha(C)

File <string>:9, in __init__(self, C, g)

AttributeError: 'as_cover' object has no attribute 'polynomial'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l....:     return superelliptic_function(C, (f2/f1).nth_root(2))

....: [?7h[?12l[?25h[?25l[?7lsage: def alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     return superelliptic_function(C, (f2/f1).nth_root(2))

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.nth_root(p)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: alpha(C)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [7], line 1
----> 1 alpha(C)

Cell In [6], line 4, in alpha(C)
      2 f1, f2 = C.functions
      3 f1, f2 = f1.function, f2.function
----> 4 return superelliptic_function(C, (f2/f1).nth_root(Integer(2)))

File <string>:9, in __init__(self, C, g)

AttributeError: 'as_cover' object has no attribute 'polynomial'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     print(f1, f2, (f2/f1).nth_root(2))

....:     return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l....:     return superelliptic_function(C, (f2/f1).nth_root(2))

....: [?7h[?12l[?25h[?25l[?7lsage: def alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     print(f1, f2, (f2/f1).nth_root(2))

....:     return superelliptic_function(C, (f2/f1).nth_root(2))

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: alpha(C)

[?7h[?12l[?25h[?2004lx^5 x^13 x^4
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [9], line 1
----> 1 alpha(C)

Cell In [8], line 5, in alpha(C)
      3 f1, f2 = f1.function, f2.function
      4 print(f1, f2, (f2/f1).nth_root(Integer(2)))
----> 5 return superelliptic_function(C, (f2/f1).nth_root(Integer(2)))

File <string>:9, in __init__(self, C, g)

AttributeError: 'as_cover' object has no attribute 'polynomial'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lspan(v1, v2)[?7h[?12l[?25h[?25l[?7lum(floor(305/5^n) for n in range(1, 10))[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     Fxyz, Rxyz, x, y, z = C.fct_field

....:     print(f1, f2, (f2/f1).nth_root(2))

....:     return superelliptic_function(C, Fxyz((f2/f1).nth_root(2)))[?7h[?12l[?25h[?25l[?7l....:     return superelliptic_function(C, Fxyz((f2/f1).nth_root(2)))

....: [?7h[?12l[?25h[?25l[?7lsage: def alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     Fxyz, Rxyz, x, y, z = C.fct_field

....:     print(f1, f2, (f2/f1).nth_root(2))

....:     return superelliptic_function(C, Fxyz((f2/f1).nth_root(2)))

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: alpha(C)

[?7h[?12l[?25h[?2004lx^5 x^13 x^4
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [11], line 1
----> 1 alpha(C)

Cell In [10], line 6, in alpha(C)
      4 Fxyz, Rxyz, x, y, z = C.fct_field
      5 print(f1, f2, (f2/f1).nth_root(Integer(2)))
----> 6 return superelliptic_function(C, Fxyz((f2/f1).nth_root(Integer(2))))

File <string>:9, in __init__(self, C, g)

AttributeError: 'as_cover' object has no attribute 'polynomial'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004lTrue
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [12], line 8
      6 BASIS += [aux]
      7 #
----> 8 aux = superelliptic_cech(C, C.z[Integer(1)]*C.x**i*C.dx, C.z[Integer(0)]*C.z[Integer(1)]*alpha/(C.x**(M - Integer(1) - i) + alpha * C.x**(m - Integer(1) - i)))
      9 print(aux.omega8.valuation() > Integer(0))
     10 BASIS += [aux]

TypeError: unsupported operand type(s) for /: 'NoneType' and 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha = x^((M - m)/2)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: alpha

[?7h[?12l[?25h[?2004l[?7hx^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
True
True
True
False
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [14], line 41
     39 lista = []
     40 for a in BASIS:
---> 41     lista += a.coordinates(basis = BB)
     43 V = F**(Integer(2)*C.genus())
     44 print(V.subspace(lista).dimension())

NameError: name 'BB' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = C.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: BB BOmega = C.holomorphic_differentials_basis()

....: BOX = C.cohomology_of_structure_sheaf_basis()

....: BB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BB BOmega = C.holomorphic_differentials_basis()

....: BOX = C.cohomology_of_structure_sheaf_basis()

....: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l  Cell In [15], line 1
    BB BOmega = C.holomorphic_differentials_basis()
       ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

....: BOX = C.cohomology_of_structure_sheaf_basis()

....: BB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lsage: BOmega = C.holomorphic_differentials_basis()

....: BOX = C.cohomology_of_structure_sheaf_basis()

....: BB = [BOmega, BOX, B]

[?7h[?12l[?25h[?2004l
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
True
True
True
False
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [17], line 41
     39 lista = []
     40 for a in BASIS:
---> 41     lista += a.coordinates(basis = BB)
     43 V = F**(Integer(2)*C.genus())
     44 print(V.subspace(lista).dimension())

TypeError: superelliptic_cech.coordinates() got an unexpected keyword argument 'basis'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004lTrue
True
True
True
True
True
True
True
True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [18], line 17
     14     BASIS += [aux]
     16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)):
---> 17     aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i))
     18     print(aux.omega8.valuation() > Integer(0))
     19     BASIS += [aux]

File <string>:18, in __init__(self, C, omega, f)

ValueError: cech cocycle not regular
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004l1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
2A,  2 True
2B,  2 True
2C,  2 True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [19], line 17
     14     BASIS += [aux]
     16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)):
---> 17     aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i))
     18     print("2A, ", i, aux.omega8.valuation() > Integer(0))
     19     BASIS += [aux]

File <string>:18, in __init__(self, C, omega, f)

ValueError: cech cocycle not regular
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1):

....:     try:

....:         aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

....:         print("2A, ", i, aux.omega8.valuation() > 0)

....:         BASIS += [aux]

....:         #

....:         aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

....:         print("2B, ", i, aux.omega8.valuation() > 0)

....:         BASIS += [aux]

....:         #

....:         aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:         print("2C, ", i, aux.omega8.valuation() > 0)

....:         BASIS += [aux]

....:     except:

....:         pass[?7h[?12l[?25h[?25l[?7l....:         pass

....: [?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1):

....:     try:

....:         aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

....:         print("2A, ", i, aux.omega8.valuation() > 0)

....:         BASIS += [aux]

....:         #

....:         aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

....:         print("2B, ", i, aux.omega8.valuation() > 0)

....:         BASIS += [aux]

....:         #

....:         aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:         print("2C, ", i, aux.omega8.valuation() > 0)

....:         BASIS += [aux]

....:     except:

....:         pass

....: 

[?7h[?12l[?25h[?2004l2A,  2 True
2B,  2 True
2C,  2 True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1):

....:     #aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

....:     #print("2A, ", i, aux.omega8.valuation() > 0)

....:     #BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

....:     print("2B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux][?7h[?12l[?25h[?25l[?7l....:     BASIS += [aux]

....: [?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1):

....:     #aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

....:     #print("2A, ", i, aux.omega8.valuation() > 0)

....:     #BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

....:     print("2B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

[?7h[?12l[?25h[?2004l2B,  2 True
2C,  2 True
2B,  3 True
2C,  3 True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_M32(B[-3], BB)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: i = 3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lmC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l=C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range((m-1)/2, m - 1):[?7h[?12l[?25h[?25l[?7lf.coordintes)[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7l = C.z[0]/C.x^3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[]C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l()C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[]C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lC.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[0]*C.z[1]/C.x^(m-1-i)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om - fff.diffn()

[?7h[?12l[?25h[?2004l[?7h(z0*z1/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - fff.diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om - f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (om - fff.diffn()).valuation()

[?7h[?12l[?25h[?2004l[?7h-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: lift

 lift            

 lift_form_to_drw

 lift_to_sl2z    



 [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x^5*z0 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^3*z0) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^4*z0) * dx, 0 ),
 ( (x^5) * dx, 0 ),
 ( (x^6) * dx, 0 ),
 ( (x^11) * dx, z1/x ),
 ( (0) * dx, z0/x ),
 ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ),
 ( (x^10) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ),
 ( (x^9) * dx, z1/x^3 ),
 ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ),
 ( (x^8) * dx, z1/x^4 ),
 ( (x^8*z0 + z1) * dx, z0*z1/x^4 ),
 ( (x^7) * dx, z1/x^5 ),
 ( (x^7*z0) * dx, z0*z1/x^5 ),
 ( (x^6*z0) * dx, z0*z1/x^6 ),
 ( (x^5*z0) * dx, z0*z1/x^7 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l(om - fff.diffn()).valuation()[?7h[?12l[?25h[?25l[?7lom - f.difn()[?7h[?12l[?25h[?25l[?7l(om - f.difn()).valuation()[?7h[?12l[?25h[?25l[?7lom - f.difn()[?7h[?12l[?25h[?25l[?7lsage: om - fff.diffn()

[?7h[?12l[?25h[?2004l[?7h(z0*z1/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om - fff.diffn()).valuation()[?7h[?12l[?25h[?25l[?7lC.z[1]/Cx^3*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[1]/C.x^5).diffn()

[?7h[?12l[?25h[?2004l[?7h((x^13 + z1)/x^6) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.z[1]/C.x^6)*C.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(*)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: ((C.z[1]/C.x^6)*C.dx).valuation()

[?7h[?12l[?25h[?2004l[?7h24
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx_series[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^7*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^7*C.dx).valuation()

[?7h[?12l[?25h[?2004l[?7h-2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lzC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]0C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lzC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l1C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[]/C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l.C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lxC.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l^C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l2C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l+C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lX + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l. + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7ld + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]*C.z[1]/C.x^2*C.dx + C.x^7*C.dx).valuation()

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1]/C.x^2*C.dx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z[0]*C.z[1]/C.x^2*C.dx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]*C.z[1] + alpha*f1).valuation()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [33], line 1
----> 1 (C.z[Integer(0)]*C.z[Integer(1)] + alpha*f1).valuation()

File <string>:23, in __add__(self, other)

AttributeError: 'NoneType' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1] + alpha*f1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7lC).valuation()[?7h[?12l[?25h[?25l[?7l.).valuation()[?7h[?12l[?25h[?25l[?7lx).valuation()[?7h[?12l[?25h[?25l[?7l^).valuation()[?7h[?12l[?25h[?25l[?7lm).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.z[0]*C.z[1] + alpha*C.x^m).valuation()

[?7h[?12l[?25h[?2004l[?7h-31
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: -m - 2*M

[?7h[?12l[?25h[?2004l[?7h-31
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-m - 2*M[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1] + alpha*C.x^m).valuation()[?7h[?12l[?25h[?25l[?7lf1).valution()[?7h[?12l[?25h[?25l[?7l/C.x^2*C.dx + C.x^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lx^7*C.dx).valuation()[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^6)*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC.z[1]/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7lom - fff.diffn()[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l(om - fff.diffn()).valuation()[?7h[?12l[?25h[?25l[?7lom - f.difn()[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7lsage: for i in range((m-1)/2, m - 1):

....:     #aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

....:     #print("2A, ", i, aux.omega8.valuation() > 0)

....:     #BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

....:     print("2B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

try:

    aux = as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

    print("2A, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]

   #

    aux = as_cech(C, C.x^(M - m + )*C.dx, C.z[1]/C.x^(m-1-i))

    print("2B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]

   #

    aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:         print("2C, ", i, aux.omega8.valuation() > 0)

....:         BASIS += [aux]

....:     except:

....:         pass[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:    aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

BASIS += [ux]



foriin range((m-1)/2, M - (m+3)/2 + 1):

aux= as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuaton() > 0)

BASIS += [aux]

#

aux= as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]





....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)



V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)

[?7h[?12l[?25h[?25l[?7lprint("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:[?7h[?12l[?25h[?25l[?7l#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]





list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



[?7h[?12l[?25h[?25l[?7lprint("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3B, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l

fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print("3A, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux]

[?7h[?12l[?25h[?25l[?7laux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7l#

aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))

print("2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lprint("1A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7laux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print("2B, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS= []

fori in range(0, (m-1)/2):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2)

BASIS= []

fori in range(0, (m-1)/2):

aux = as_cech(CC.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print("1B, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = as_cech(CC.^i*C.dx, 0*C.x)

print("1C, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = as_cech(CC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print("2A, ", i, aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7l....:     ux= as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

    print(aux.omega8.valuation() > 0)

   BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux =as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]





lista = []

aBASIS:

lista+= a.oordinates(basis = BB)



V=F^(2*C.genus())

print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l[]

()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l[]

()[?7h[?12l[?25h[?25l[?7l#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)



V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)

[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:[?7h[?12l[?25h[?25l[?7l#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l

fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

aux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]

[?7h[?12l[?25h[?25l[?7l#

aux =as_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =as_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

   BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux =as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

    print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7laux =as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =as_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =as_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

   BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux =as_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux][?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lBASIS= []

fori in range(0, (m-1)/2):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2)

BASIS= []

fori in range(0, (m-1)/2):

aux = s_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = s_cech(C, C.x^i*C.dx,0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = s_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7l....:     ux= superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

    print(aux.omega8.valuation() > 0)

   BASIS += [aux]



fori in range((m-1)/2, M - (m+3)/2 + 1):

aux =superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]





lista = []

aBASIS:

lista+= a.oordinates(basis = BB)



V=F^(2*C.genus())

print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)



V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)

[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l

fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]

[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

   BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux =superelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

    print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS= []

fori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2)

BASIS= []

fori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7lBOmega = C.holomorphic_differentials_basis()

OX =C.cohomology_of_structure_sheaf_basis()

BB = [BOmega, BOX, B]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB BOmega = C.holomorphic_differentials_basis()



[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:    aux =supereliptic_ech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

   print(aux.omega8.valuation() > 0)

   BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)



V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)

[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l

fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]

[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

   BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux =superelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

    print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS= []

fori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lsage: alphaC.x^((M - m)/2)

BASIS= []

fori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l....:     ux = superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = superelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = superelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print(aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()

[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)



V = F^(2*C.genus))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)

[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:

    lista += a.coordinates(basis = BB)[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= []

fora in BASIS:[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]





list= [][?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

    BASIS += [aux][?7h[?12l[?25h[?25l[?7lfori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l

fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]



fori in range((m-1)/2, M - m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

    BASIS += [aux]

[?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

   BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux =superelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS+= [aux]

#

aux =superelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

    print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lprint(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7laux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lfori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))[?7h[?12l[?25h[?25l[?7lBASIS= []

fori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#[?7h[?12l[?25h[?25l[?7lsage: alphax^((M - m)/2)

BASIS= []

fori in range(0, (m-1)/2):

aux = sperelliptic_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i)))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

    aux = superelliptic_cech(C, C.z[1]*C.x^i*C.dx, C.z[0]*C.z[1]*alpha/(C.x^(M - 1 - i) + alpha * C.x^(m - 1 - i
)

))

print(aux.omega8.valuation() > 0)

BASIS += [aux]

#

aux = sperelliptic_cech(C, C.x^i*C.dx, 0*C.x)

print(aux.omega8.valuation() > 0)

BASIS += [aux]



fori in range((m-1)/2, m - 1):

aux = sperelliptic_cech(C, C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx, C.z[0]*C.z[1]/C.x^(m-1-i))

print(aux.omega8.valuation() > 0)

BASIS += [aux][?7h[?12l[?25h[?25l[?7l(C)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7ldef alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     Fxyz, Rxyz, x, y, z = C.fct_field

....:     print(f1, f2, (f2/f1).nth_root(2))

....:     return superelliptic_function(C, Fxyz((f2/f1).nth_root(2)))[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C)

 

 

 

 

 [?7h[?12l[?25h[?25l[?7ldef alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     print(f1, f2, (f2/f1).nth_root(2))

....:     return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha(C)

 

 

 

 [?7h[?12l[?25h[?25l[?7ldef alpha(C):

....:     f1, f2 = C.functions

....:     f1, f2 = f1.function, f2.function

....:     return superelliptic_function(C, (f2/f1).nth_root(2))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')

 

 

 [?7h[?12l[?25h[?25l[?7lf.nth_root(2)[?7h[?12l[?25h[?25l[?7l = x^6[?7h[?12l[?25h[?25l[?7lRx.<> = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7lC.holomorphic_differetials_basis()[?7h[?12l[?25h[?25l[?7l(C.z[1]/C.x^3*C.dx).valution()[?7h[?12l[?25h[?25l[?7lxiomega8[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7l = superelipc_cech(C, C.z[0]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8.valuation()[?7h[?12l[?25h[?25l[?7lcoordinates(basis = B, threshold = 20)[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, C.z[1]*C.x^9*C.dx, C.z[0] * C.z[1] * (C.one + C.x^4)/C.x^7)[?7h[?12l[?25h[?25l[?7l(C.z[1]*C.x*C.dx).valuation()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lfor e in W1.intersection(W2).intersection(V1).basis():

....:     n = len(list(e))

....:     print(from_coor(e, B))

....:     A3 = block_matrix([[A1 - I], [A2 - I]])

....:     e = list(e) + n*[0]

....:     e = vector(F, e)

....:     try:

....:         print('e2', from_coor(A3.solve_right(e), B))

....:     except:

....:         pass[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l











print('e2', A3.solve_right(e))

 

 

 [?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l[]

()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lB:

   if is_M32(e, BB):

         print(e, gene(e))

 

 

 

 [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldefgene(x):

y1=x - x.group_action([0, 1])

y2=x-x.group_action([1, 0])

....:     return(y1, y2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfore in B:

   if is_M32(e, BB):

     print(e, gene(e))

 [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l



(gene(e))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBB = [BOmega, BOX, B]

 

 [?7h[?12l[?25h[?25l[?7lOmega = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = [BOmega, BOX, B][?7h[?12l[?25h[?25l[?7lfor e in B:

....:          if is_M32(e, BB):

....:              print(gene(e))[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7le, gene(e))[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7ldefgene(x):

y1=x - x.group_action([0, 1])

y2=x-x.group_action([1, 0])

....:     return(y1, y2)[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7lfore in B:

   if is_M32(e, BB):

     print(e, gene(e))

 [?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7lprint(e, gene(e)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^13*z0 + x^5*z1 + z0*z1)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

































 [?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff

[?7h[?12l[?25h[?2004l[?7hz0*z1/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





























 [?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7lsage: i

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

























 [?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004l1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [39], line 17
     14     BASIS += [aux]
     16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)):
---> 17     aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*f1/C.x**(i+Integer(1) - M - m))
     18     print("2A, ", i, aux.omega8.valuation() > Integer(0))
     19     BASIS += [aux]

TypeError: unsupported operand type(s) for /: 'NoneType' and 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print("2A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

....:     print("2B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: [?7h[?12l[?25h[?25l[?7l....:     print("2A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^(M - m + i)*C.dx, C.z[1]/C.x^(m-1-i))

....:     print("2B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

[?7h[?12l[?25h[?2004l1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [40], line 17
     14     BASIS += [aux]
     16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)):
---> 17     ff1 = as_function(C, f1.polynomial)
     18     aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))
     19     print("2A, ", i, aux.omega8.valuation() > Integer(0))

AttributeError: 'superelliptic_function' object has no attribute 'polynomial'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004l1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [41], line 18
     16 for i in range((m-Integer(1))/Integer(2), m - Integer(1)):
     17     ff1 = as_function(C, f1.function)
---> 18     aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))
     19     print("2A, ", i, aux.omega8.valuation() > Integer(0))
     20     BASIS += [aux]

File <string>:18, in __init__(self, C, omega, f)

ValueError: cech cocycle not regular
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = 3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: i = 3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Intege
r

....: (1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))[?7h[?12l[?25h[?25l[?7l(

)a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Intege
r

....: (1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))aaed

[?7h[?12l[?25h[?2004l  Cell In [43], line 1
    aux = as_cech(C, C.z[Integer(Integer(1))]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(Integer(0))]*C.dx, C.z[Integer(Integer(0))]*C.z[Integer(Integer(1))]/C.x**(m-Integer(Integer(1))-i) + C.z[Integer(Integer(1))]*alpha*ff1/C.x**(i+Integer(Integer(1)) - M - m))aaed
                                                                                                                                                                                                                                                                       ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - fff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]/C.x^(m-1-i)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -

....: m)[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -

....: m)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -
 

....: m)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()

 [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -
 

....: m)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff

[?7h[?12l[?25h[?2004l[?7h(x^24*z1 + z0*z1)/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^5
z1^2 - z1 = x^13

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = as_cech(C, C.z[Integer(1)]*C.x**i*C.dx + C.x**(M - m + i)*C.z[Integer(0)]*C.dx, C.z[Integer(0)]*C.z[Intege
r

....: (1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M - m))aaed[?7h[?12l[?25h[?25l[?7llpha= C.x^(M - m)/2)

 [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: alpha

[?7h[?12l[?25h[?2004l[?7hx^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: ff0

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [49], line 1
----> 1 ff0

NameError: name 'ff0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff0[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: ff1

[?7h[?12l[?25h[?2004l[?7hx^5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff1[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^37 + x^24*z1 + x^13*z0 + x^5*z1 + z0*z1)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: alpha*f0

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [52], line 1
----> 1 alpha*f0

NameError: name 'f0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha*f0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: alpha*ff1

[?7h[?12l[?25h[?2004l[?7hx^9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[Integer(0)]*C.z[Integer(1)]/C.x**(m-Integer(1)-i) + C.z[Integer(1)]*alpha*ff1/C.x**(i+Integer(1) - M -
 

....: m)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1

 [?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[1]/C.x^6

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn()

[?7h[?12l[?25h[?2004l[?7h(x^6) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[1]/C.x^6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]C.x^6[?7h[?12l[?25h[?25l[?7l[]*C.x^6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[1]*C.x^23

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[1]*C.x^23[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn()

[?7h[?12l[?25h[?2004l[?7h(x^35 + x^22*z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[1]*C.x^23[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]C.x^23[?7h[?12l[?25h[?25l[?7l[]/C.x^23[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: fff = C.z[1]/C.x^5

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = C.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^13 + z1)/x^6) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7l....:     aux = as_cech(C, C.x^i*C.dx, C.z[0]/C.x^(m-1-i))

....:     print("2C, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: for i in range((m-1)/2, M - (m+3)/2 + 1):

....:     aux = as_cech(C, C.z[0]*C.x^i*C.dx, C.z[0]*C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3A, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....:     #

....:     aux = as_cech(C, C.x^i*C.dx, C.z[1]/(C.x^(M-1-i) + alpha * C.x^(m-i-1)))

....:     print("3B, ", i, aux.omega8.valuation() > 0)

....:     BASIS += [aux]

....: 

....: 

....: lista = []

....: for a in BASIS:

....:     lista += a.coordinates(basis = BB)

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004l1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
2A,  2 True
2B,  2 True
2C,  2 True
2A,  3 True
2B,  3 True
2C,  3 True
3A,  2 True
3B,  2 True
3A,  3 True
3B,  3 True
3A,  4 True
3B,  4 True
3A,  5 True
3B,  5 True
3A,  6 True
3B,  6 True
3A,  7 True
3B,  7 True
3A,  8 True
3B,  8 True
3A,  9 True
3B,  9 True
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.8/src/sage/modules/free_module.py:6488, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category)
   6487 try:
-> 6488     basis = [ambient(x) for x in basis]
   6489 except TypeError:
   6490     # That failed, try the ambient vector space instead

File /ext/sage/9.8/src/sage/modules/free_module.py:6488, in <listcomp>(.0)
   6487 try:
-> 6488     basis = [ambient(x) for x in basis]
   6489 except TypeError:
   6490     # That failed, try the ambient vector space instead

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    895 if no_extra_args:
--> 896     return mor._call_(x)
    897 else:

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.8/src/sage/modules/free_module.py:6355, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
   6354     pass
-> 6355 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)

File /ext/sage/9.8/src/sage/modules/free_module.py:2161, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
   2160 if isinstance(self, FreeModule_ambient):
-> 2161     return self.element_class(self, x, coerce, copy)
   2162 try:

File /ext/sage/9.8/src/sage/modules/vector_mod2_dense.pyx:213, in sage.modules.vector_mod2_dense.Vector_mod2_dense.__init__()
    212 elif x != 0:
--> 213     raise TypeError("can't initialize vector from nonzero non-list")
    214 elif self._degree:

TypeError: can't initialize vector from nonzero non-list

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
File /ext/sage/9.8/src/sage/modules/free_module.py:6494, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category)
   6493 try:
-> 6494     basis = [V(x) for x in basis]
   6495 except TypeError:

File /ext/sage/9.8/src/sage/modules/free_module.py:6494, in <listcomp>(.0)
   6493 try:
-> 6494     basis = [V(x) for x in basis]
   6495 except TypeError:

File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
    895 if no_extra_args:
--> 896     return mor._call_(x)
    897 else:

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:

File /ext/sage/9.8/src/sage/modules/free_module.py:6355, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
   6354     pass
-> 6355 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)

File /ext/sage/9.8/src/sage/modules/free_module.py:2161, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
   2160 if isinstance(self, FreeModule_ambient):
-> 2161     return self.element_class(self, x, coerce, copy)
   2162 try:

File /ext/sage/9.8/src/sage/modules/vector_mod2_dense.pyx:213, in sage.modules.vector_mod2_dense.Vector_mod2_dense.__init__()
    212 elif x != 0:
--> 213     raise TypeError("can't initialize vector from nonzero non-list")
    214 elif self._degree:

TypeError: can't initialize vector from nonzero non-list

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Cell In [60], line 45
     42     lista += a.coordinates(basis = BB)
     44 V = F**(Integer(2)*C.genus())
---> 45 print(V.subspace(lista).dimension())

File /ext/sage/9.8/src/sage/modules/free_module.py:4663, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized)
   4620 def subspace(self, gens, check=True, already_echelonized=False):
   4621     """
   4622     Return the subspace of ``self`` spanned by the elements of gens.
   4623 
   (...)
   4661         ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self
   4662     """
-> 4663     return self.submodule(gens, check=check, already_echelonized=already_echelonized)

File /ext/sage/9.8/src/sage/modules/free_module.py:1745, in Module_free_ambient.submodule(self, gens, check, already_echelonized)
   1743 if isinstance(gens, Module_free_ambient):
   1744     gens = gens.gens()
-> 1745 V = self.span(gens, check=check, already_echelonized=already_echelonized)
   1746 if check:
   1747     if not V.is_submodule(self):

File /ext/sage/9.8/src/sage/modules/free_module.py:1660, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized)
   1658     gens = gens.gens()
   1659 if base_ring is None or base_ring is self.base_ring():
-> 1660     return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized)
   1662 # The base ring has changed
   1663 try:

File /ext/sage/9.8/src/sage/modules/free_module.py:7914, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized, category)
   7912 if is_FreeModule(gens):
   7913     gens = gens.gens()
-> 7914 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check,
   7915     echelonize=not already_echelonized, already_echelonized=already_echelonized,
   7916     category=category)

File /ext/sage/9.8/src/sage/modules/free_module.py:7714, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category)
   7698 def __init__(self, ambient, basis, check=True,
   7699     echelonize=False, echelonized_basis=None, already_echelonized=False,
   7700     category=None):
   7701     """
   7702     Create a vector space with given basis.
   7703 
   (...)
   7712         [4 5 6]
   7713     """
-> 7714     FreeModule_submodule_with_basis_pid.__init__(
   7715         self, ambient, basis=basis, check=check, echelonize=echelonize,
   7716         echelonized_basis=echelonized_basis, already_echelonized=already_echelonized,
   7717         category=category)

File /ext/sage/9.8/src/sage/modules/free_module.py:6496, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized, category)
   6494         basis = [V(x) for x in basis]
   6495     except TypeError:
-> 6496         raise TypeError("each element of basis must be in "
   6497                         "the ambient vector space")
   6499 if echelonize and not already_echelonized:
   6500     basis = self._echelonized_basis(ambient, basis)

TypeError: each element of basis must be in the ambient vector space
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7lsage: lista

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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7len(Z[0])[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: len(lista)

[?7h[?12l[?25h[?2004l[?7h784
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(lista)[?7h[?12l[?25h[?25l[?7lista[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lsage: lista2 = [

....: [?7h[?12l[?25h[?25l[?7l[

][?7h[?12l[?25h[?25l[?7lsage: lista2 = [

....: ]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista2 = [[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.genus()

[?7h[?12l[?25h[?2004l[?7h28
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7*2 + 1[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l784.[?7h[?12l[?25h[?25l[?7l784[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: 784/28

[?7h[?12l[?25h[?2004l[?7h28
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lista = []

....: for a in BASIS:

....:     lista += [a.coordinates(basis = BB)]

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7lsage: lista = []

....: for a in BASIS:

....:     lista += [a.coordinates(basis = BB)]

....: 

....: V = F^(2*C.genus())

....: print(V.subspace(lista).dimension())

[?7h[?12l[?25h[?2004l28
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS = [][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: BASIS

[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^8) ),
 ( (z1) * dx, z0*z1/(x^8 + x^4) ),
 ( (1) * dx, 0 ),
 ( (x*z0) * dx, z0*z1/(x^11 + x^7) ),
 ( (x*z1) * dx, z0*z1/(x^7 + x^3) ),
 ( (x) * dx, 0 ),
 ( (x^10*z0 + x^2*z1) * dx, (x^4*z0*z1 + z1)/x^6 ),
 ( (x^10) * dx, z1/x^2 ),
 ( (x^2) * dx, z0/x^2 ),
 ( (x^11*z0 + x^3*z1) * dx, (x^4*z0*z1 + z1)/x^5 ),
 ( (x^11) * dx, z1/x ),
 ( (x^3) * dx, z0/x ),
 ( (x^2*z0) * dx, z0*z1/(x^10 + x^6) ),
 ( (x^2) * dx, z1/(x^10 + x^6) ),
 ( (x^3*z0) * dx, z0*z1/(x^9 + x^5) ),
 ( (x^3) * dx, z1/(x^9 + x^5) ),
 ( (x^4*z0) * dx, z0*z1/(x^8 + x^4) ),
 ( (x^4) * dx, z1/(x^8 + x^4) ),
 ( (x^5*z0) * dx, z0*z1/(x^7 + x^3) ),
 ( (x^5) * dx, z1/(x^7 + x^3) ),
 ( (x^6*z0) * dx, z0*z1/(x^6 + x^2) ),
 ( (x^6) * dx, z1/(x^6 + x^2) ),
 ( (x^7*z0) * dx, z0*z1/(x^5 + x) ),
 ( (x^7) * dx, z1/(x^5 + x) ),
 ( (x^8*z0) * dx, z0*z1/(x^4 + 1) ),
 ( (x^8) * dx, z1/(x^4 + 1) ),
 ( (x^9*z0) * dx, x*z0*z1/(x^4 + 1) ),
 ( (x^9) * dx, x*z1/(x^4 + 1) )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin BASIS:[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....: [?7h[?12l[?25h[?25l[?7lprint("3B, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7laux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lO[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(a.f.coordinates(basis = BOX))

....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....:     print(a.f.coordinates(basis = BOX))

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [68], line 2
      1 for a in BASIS:
----> 2     print(a.f.coordinates(basis = BOX))

File <string>:149, in coordinates(self, prec, basis)

TypeError: 'as_function' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....:     print(a.f.coordinates(basis = BOX))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(a.f.coordinates())

....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....:     print(a.f.coordinates())

....: 

[?7h[?12l[?25h[?2004l[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la in BASIS:[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....: [?7h[?12l[?25h[?25l[?7lif len(V.linear_dependence([y1_coor, y2_coor])) > 0:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

....: for a in BASIS:

....:     if a.f.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv28*[0][?7h[?12l[?25h[?25l[?7le28*[0][?7h[?12l[?25h[?25l[?7lc28*[0][?7h[?12l[?25h[?25l[?7lt28*[0][?7h[?12l[?25h[?25l[?7lo28*[0][?7h[?12l[?25h[?25l[?7lr28*[0][?7h[?12l[?25h[?25l[?7l(28*[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF28*[0])[?7h[?12l[?25h[?25l[?7l,28*[0])[?7h[?12l[?25h[?25l[?7l 28*[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()"[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:     if a.f.coordinates() == vector(F, 28*[0]):

....: [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l....:         licz += 1

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(V.subspace(lista).dimension())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: licz = 0

....: for a in BASIS:

....:     if a.f.coordinates() == vector(F, 28*[0]):

....:         licz += 1

....: print(licz)

[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0

....: for a in BASIS:

....:     if a.f.coordinates() == vector(F, 28*[0]):

....:         licz += 1

....: print(licz)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lla.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7lia.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7lsa.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7lta.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7llist(a.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7llista.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7la.f.cordinates() = vector(F, 28*[0]):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[0]):[?7h[?12l[?25h[?25l[?7l*[0]):[?7h[?12l[?25h[?25l[?7l1*[0]):[?7h[?12l[?25h[?25l[?7l4*[0]):[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0

....: for a in BASIS:

....:     if a.f.coordinates() == vector(F, 14*[0]):

....:         licz += 1

....: print(licz)

[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0

....: for a in BASIS:

....:     if a.f.coordinates() == vector(F, 14*[0]):

....:         licz += 1

....: print(licz)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l14*[0]):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lla.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7lia.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7lsa.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7lta.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7llist(a.f.cordinates() = 14*[0]:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()) = 14*[0]:[?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0

....: for a in BASIS:

....:     if list(a.f.coordinates()) == 14*[0]:

....:         licz += 1

....: print(licz)

[?7h[?12l[?25h[?2004l12
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: licz = 0

....: for a in BASIS:

....:     if list(a.f.coordinates()) == 14*[0]:

....:         licz += 1

....: print(licz)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l



a.f.coordinates() == vector(F, 14*[0]):



()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l



28



()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:

   print(a.f.coordinates())

 

 

 [?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....:     print(a.f.coordinates())

....: 

[?7h[?12l[?25h[?2004l[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
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[?7h[?12l[?25h[?2004l[?7h( (x*z1) * dx, z0*z1/(x^7 + x^3) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[4][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[-10]

[?7h[?12l[?25h[?2004l[?7h( (x^5*z0) * dx, z0*z1/(x^7 + x^3) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicz = 0[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

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[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 0]
[1 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^8 ) ( (x*z0) * dx, 0 )
(0) * dx ((x^6*z0 + z1)/x^2) * dx (0) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
(0) * dx ((x^13*z0 + x^7*z1 + z0*z1)/x^8) * dx (0) * dx
1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
1A,  2 True
1B,  2 True
1C,  2 True
2A,  3 True
2B,  3 True
2C,  3 True
2A,  4 False
2B,  4 True
2C,  4 True
2A,  5 True
2B,  5 True
2C,  5 True
3A,  3 True
3B,  3 True
3A,  4 True
3B,  4 True
3A,  5 True
3B,  5 True
3A,  6 True
3B,  6 True
3A,  7 True
3B,  7 True
3A,  8 True
3B,  8 True
30
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[-10][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l`[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[12]

[?7h[?12l[?25h[?2004l[?7h( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[12][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: BASIS[12].omega8.valuation() >= 0

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l in BASIS:[?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....: [?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7l....:     print(a.f.coordinates())

....: [?7h[?12l[?25h[?25l[?7lsage: for a in BASIS:

....:     print(a.f.coordinates())

....: 

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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^8 ) ( (x*z0) * dx, 0 )
(0) * dx ((x^6*z0 + z1)/x^2) * dx (0) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
(0) * dx ((x^13*z0 + x^7*z1 + z0*z1)/x^8) * dx (0) * dx
1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
1A,  2 True
1B,  2 True
1C,  2 True
2A,  3 True
2B,  3 True
2C,  3 True
2A,  4 True
2B,  4 True
2C,  4 True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [82], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:109

File <string>:18, in __init__(self, C, omega, f)

ValueError: cech cocycle not regular
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]


[1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
{
[1 0 0]
[0 1 1]
[0 0 1],
[1 0 1]
[0 1 0]
[0 0 1]
}
( (1) * dx, 0 ) ( (z1) * dx, 0 ) ( (z0) * dx, 0 )
(0) * dx (0) * dx (0) * dx
( (x) * dx, 0 ) ( (x*z1) * dx, z0*z1/x^8 ) ( (x*z0) * dx, 0 )
(0) * dx ((x^6*z0 + z1)/x^2) * dx (0) * dx
( (x^2) * dx, 0 ) ( (x^2*z1) * dx, z0*z1/x^7 ) ( (x^2*z0) * dx, 0 )
(0) * dx ((x^13*z0 + x^7*z1 + z0*z1)/x^8) * dx (0) * dx
1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
1A,  2 True
1B,  2 True
1C,  2 True
2A,  3 True
2B,  3 True
2C,  3 True
2A,  4 True
2B,  4 True
2C,  4 True
2A,  5 True
2B,  5 True
2C,  5 True
3A,  3 True
3B,  3 True
3A,  4 True
3B,  4 True
3A,  5 True
3B,  5 True
3A,  6 True
3B,  6 True
3A,  7 True
3B,  7 True
3A,  8 True
3B,  8 True
30
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h15
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [1], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:18

NameError: name 'A1' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
1A,  2 True
1B,  2 True
1C,  2 True
2A,  3 True
2B,  3 True
2C,  3 True
2A,  4 True
2B,  4 True
2C,  4 True
2A,  5 True
2B,  5 True
2C,  5 True
3A,  3 True
3B,  3 True
3A,  4 True
3B,  4 True
3A,  5 True
3B,  5 True
3A,  6 True
3B,  6 True
3A,  7 True
3B,  7 True
3A,  8 True
3B,  8 True
Tyle form powinno być: 15  Tyle jest:  14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[4][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: BASIS

[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^9) ),
 ( (z1) * dx, z0*z1/(x^9 + x^6) ),
 ( (1) * dx, 0 ),
 ( (x*z0) * dx, z0*z1/(x^11 + x^8) ),
 ( (x*z1) * dx, z0*z1/(x^8 + x^5) ),
 ( (x) * dx, 0 ),
 ( (x^2*z0) * dx, z0*z1/(x^10 + x^7) ),
 ( (x^2*z1) * dx, z0*z1/(x^7 + x^4) ),
 ( (x^2) * dx, 0 ),
 ( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 ),
 ( (x^9) * dx, z1/x^3 ),
 ( (x^3) * dx, z0/x^3 ),
 ( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 ),
 ( (x^10) * dx, z1/x^2 ),
 ( (x^4) * dx, z0/x^2 ),
 ( (x^11*z0 + x^5*z1) * dx, (x^3*z0*z1 + z1)/x^4 ),
 ( (x^11) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (x^3*z0) * dx, z0*z1/(x^9 + x^6) ),
 ( (x^3) * dx, z1/(x^9 + x^6) ),
 ( (x^4*z0) * dx, z0*z1/(x^8 + x^5) ),
 ( (x^4) * dx, z1/(x^8 + x^5) ),
 ( (x^5*z0) * dx, z0*z1/(x^7 + x^4) ),
 ( (x^5) * dx, z1/(x^7 + x^4) ),
 ( (x^6*z0) * dx, z0*z1/(x^6 + x^3) ),
 ( (x^6) * dx, z1/(x^6 + x^3) ),
 ( (x^7*z0) * dx, z0*z1/(x^5 + x^2) ),
 ( (x^7) * dx, z1/(x^5 + x^2) ),
 ( (x^8*z0) * dx, z0*z1/(x^4 + x) ),
 ( (x^8) * dx, z1/(x^4 + x) )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x^4*z0 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx,
 (x^5*z0 + x^2*z1) * dx,
 (x^2*z0) * dx,
 (x^3) * dx,
 (x^3*z0) * dx,
 (x^4) * dx,
 (x^5) * dx,
 (x^6) * dx,
 (x^7) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lbC.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1:[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: for b in BASIS:

....: [?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif list(a.f.coordinates()) == 14*[0]:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:     if b.f.valuation() >= 0:

....: [?7h[?12l[?25h[?25l[?7lpass[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreturn False[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l"2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l("2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l("2C, ", i, aux.omega8.valuation() > 0)[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:         print(b.omega0)

....: [?7h[?12l[?25h[?25l[?7lsage: for b in BASIS:

....:     if b.f.valuation() >= 0:

....:         print(b.omega0)

....: 

[?7h[?12l[?25h[?2004l(z0) * dx
(1) * dx
(x*z0) * dx
(x) * dx
(x^2*z0) * dx
(x^2) * dx
(x^3) * dx
(x^4) * dx
(x^5) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: BASIS

[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^9) ),
 ( (z1) * dx, z0*z1/(x^9 + x^6) ),
 ( (1) * dx, 0 ),
 ( (x*z0) * dx, z0*z1/(x^11 + x^8) ),
 ( (x*z1) * dx, z0*z1/(x^8 + x^5) ),
 ( (x) * dx, 0 ),
 ( (x^2*z0) * dx, z0*z1/(x^10 + x^7) ),
 ( (x^2*z1) * dx, z0*z1/(x^7 + x^4) ),
 ( (x^2) * dx, 0 ),
 ( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 ),
 ( (x^9) * dx, z1/x^3 ),
 ( (x^3) * dx, z0/x^3 ),
 ( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 ),
 ( (x^10) * dx, z1/x^2 ),
 ( (x^4) * dx, z0/x^2 ),
 ( (x^11*z0 + x^5*z1) * dx, (x^3*z0*z1 + z1)/x^4 ),
 ( (x^11) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (x^3*z0) * dx, z0*z1/(x^9 + x^6) ),
 ( (x^3) * dx, z1/(x^9 + x^6) ),
 ( (x^4*z0) * dx, z0*z1/(x^8 + x^5) ),
 ( (x^4) * dx, z1/(x^8 + x^5) ),
 ( (x^5*z0) * dx, z0*z1/(x^7 + x^4) ),
 ( (x^5) * dx, z1/(x^7 + x^4) ),
 ( (x^6*z0) * dx, z0*z1/(x^6 + x^3) ),
 ( (x^6) * dx, z1/(x^6 + x^3) ),
 ( (x^7*z0) * dx, z0*z1/(x^5 + x^2) ),
 ( (x^7) * dx, z1/(x^5 + x^2) ),
 ( (x^8*z0) * dx, z0*z1/(x^4 + x) ),
 ( (x^8) * dx, z1/(x^4 + x) )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor b in BASIS:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb in BASIS:[?7h[?12l[?25h[?25l[?7lsage: for b in BASIS:

....: [?7h[?12l[?25h[?25l[?7lprint(a.f.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lbserre_uality_pairing(om))[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(b.f.coordinates())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in BASIS:

....:     print(b.f.coordinates())

....: 

[?7h[?12l[?25h[?2004l[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lIS[?7h[?12l[?25h[?25l[?7l[4][?7h[?12l[?25h[?25l[?7l12].omega8.valuation() >= 0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[11]

[?7h[?12l[?25h[?2004l[?7h( (x^3) * dx, z0/x^3 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[11][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[-0][?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[-5]

[?7h[?12l[?25h[?2004l[?7h( (x^6) * dx, z1/(x^6 + x^3) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[-5][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BASIS[11].f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[11].f.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].f.cordinates()[?7h[?12l[?25h[?25l[?7l].f.cordinates()[?7h[?12l[?25h[?25l[?7l-].f.cordinates()[?7h[?12l[?25h[?25l[?7l5].f.cordinates()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BASIS[-5].f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[-5].f.coordinates()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: BASIS[9].f.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[9].f.coordinates()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: BASIS[9]

[?7h[?12l[?25h[?2004l[?7h( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBASIS[9][?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: BASIS

[?7h[?12l[?25h[?2004l[?7h[( (z0) * dx, z0*z1/(x^12 + x^9) ),
 ( (z1) * dx, z0*z1/(x^9 + x^6) ),
 ( (1) * dx, 0 ),
 ( (x*z0) * dx, z0*z1/(x^11 + x^8) ),
 ( (x*z1) * dx, z0*z1/(x^8 + x^5) ),
 ( (x) * dx, 0 ),
 ( (x^2*z0) * dx, z0*z1/(x^10 + x^7) ),
 ( (x^2*z1) * dx, z0*z1/(x^7 + x^4) ),
 ( (x^2) * dx, 0 ),
 ( (x^9*z0 + x^3*z1) * dx, (x^3*z0*z1 + z1)/x^6 ),
 ( (x^9) * dx, z1/x^3 ),
 ( (x^3) * dx, z0/x^3 ),
 ( (x^10*z0 + x^4*z1) * dx, (x^3*z0*z1 + z1)/x^5 ),
 ( (x^10) * dx, z1/x^2 ),
 ( (x^4) * dx, z0/x^2 ),
 ( (x^11*z0 + x^5*z1) * dx, (x^3*z0*z1 + z1)/x^4 ),
 ( (x^11) * dx, z1/x ),
 ( (x^5) * dx, z0/x ),
 ( (x^3*z0) * dx, z0*z1/(x^9 + x^6) ),
 ( (x^3) * dx, z1/(x^9 + x^6) ),
 ( (x^4*z0) * dx, z0*z1/(x^8 + x^5) ),
 ( (x^4) * dx, z1/(x^8 + x^5) ),
 ( (x^5*z0) * dx, z0*z1/(x^7 + x^4) ),
 ( (x^5) * dx, z1/(x^7 + x^4) ),
 ( (x^6*z0) * dx, z0*z1/(x^6 + x^3) ),
 ( (x^6) * dx, z1/(x^6 + x^3) ),
 ( (x^7*z0) * dx, z0*z1/(x^5 + x^2) ),
 ( (x^7) * dx, z1/(x^5 + x^2) ),
 ( (x^8*z0) * dx, z0*z1/(x^4 + x) ),
 ( (x^8) * dx, z1/(x^4 + x) )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = x^13

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: alpha

[?7h[?12l[?25h[?2004l[?7hx^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1A,  0 True
1B,  0 True
1C,  0 True
1A,  1 True
1B,  1 True
1C,  1 True
1A,  2 True
1B,  2 True
1C,  2 True
2A,  3 True
2B,  3 True
2C,  3 True
2A,  4 True
2B,  4 True
2C,  4 True
2A,  5 True
2B,  5 True
2C,  5 True
3A,  3 True
3B,  3 True
3A,  4 True
3B,  4 True
3A,  5 True
3B,  5 True
3A,  6 True
3B,  6 True
3A,  7 True
3B,  7 True
3A,  8 True
3B,  8 True
Tyle form powinno być: 15  Tyle jest:  20
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lchlogy_of_structure_hef_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

 C.cartier_matrix                      C.cohomology_of_structure_sheaf_basis

 C.characteristic                      C.crystalline_cohomology_basis       





 [?7h[?12l[?25h[?25l[?7lartier_matrix

 C.cartier_matrix                     



 <unknown> [?7h[?12l[?25h[?25l[?7lharacteristc

 C.cartier_matrix                     

 C.characteristic                     [?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis



 C.characteristic                      C.crystalline_cohomology_basis       [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lCrys of C:
( [0] d[x] + [1] d[y] + V((x^5 + x^3) dy) + dV(0), V(((x^2 + 1)/x)*y) )
( [0] d[x] + [x] d[y] + V((x^8 + 2*x^6 + 1) dy) + dV(0), [2/x*y] + V((x^4 + x^2 + 1)*y) )
Crys of C1:
( [0] d[x] + [2] d[y] + V((2*x^3 + 2*x) dy) + dV(0), V(((x^6 + x^4 + 2)/x^3)*y) )
( [0] d[x] + [2*x] d[y] + V((2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2) dy) + dV(0), V(((x^10 + x^8 + 2*x^4 + x^2 + 2)/x^4)*y) )
( [0] d[x] + [2*x^2] d[y] + V((x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3) dy) + dV(0), V(((x^12 + x^10 + 2*x^6 + x^4 + 2*x^2 + 1)/x^3)*y) )
( [0] d[x] + [2*x^3] d[y] + V((2*x^12 + 2*x^10 + x^8 + x^6 + 2*x^4 + 1) dy) + dV(0), V(((x^16 + x^14 + 2*x^10 + x^8 + 2*x^6 + x^4 + x^2 + 1)/x^4)*y) )
( [0] d[x] + [2*x^7 + 2*x] d[y] + V((2*x^32 + 2*x^30 + 2*x^24 + 2*x^22 + x^20 + x^16 + x^12 + x^10 + 2*x^8 + 2*x^2 + 1) dy) + dV(0), [2/x*y] + V(((x^26 + x^24 + 2*x^20 + x^18 + 2*x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 1)/x^2)*y) )
( [0] d[x] + [x^6 + 1] d[y] + V((x^21 + x^19 + 2*x^17 + 2*x^15 + x^13 + x^11 + 2*x^9 + x^7) dy) + dV(0), [2/x^2*y] + V(((2*x^24 + 2*x^22 + x^18 + 2*x^16 + x^14 + 2*x^12 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^4 + x^2 + 2)/x^3)*y) )
( [0] d[x] + [0] d[y] + V((2*x^8 + x^2 + 1) dy) + dV(0), [2/x^3*y] )
( [0] d[x] + [2*x^4] d[y] + V((2*x^23 + 2*x^21 + 2*x^15 + 2*x^13 + x^11 + x^7 + 2*x^3 + x) dy) + dV(0), [2/x^4*y] + V(((x^16 + x^14 + 2*x^10 + x^8 + 2*x^6 + x^4 + x^2 + 1)/x)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpsp(3, 31)> jprime(2*6, 2)^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: p]

[?7h[?12l[?25h[?2004l  Cell In [3], line 1
    p]
     ^
SyntaxError: unmatched ']'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp][?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.z[0]*C.z[1] + alpha*C.x^m).valuation()[?7h[?12l[?25h[?25l[?7lx^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3).quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(x^14 + 2*x^12 + 2*x^10 + 2*x^8 + x^6 + x^2, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha[?7h[?12l[?25h[?25l[?7ldic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: adic_expansion

 adic_expansion           

 adic_expansion_polynomial





 [?7h[?12l[?25h[?25l[?7l_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)[?7h[?12l[?25h[?25l[?7l_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)



[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lx^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x)

[?7h[?12l[?25h[?2004l[?7hx^2*t^5 + 2*x*t^4 + 2*x*t^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lxi.omega8[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x^2*((x^3 - x)^5 + (x^3 - x)^3)

[?7h[?12l[?25h[?2004l[?7hx^17 + x^15 + x^13 + 2*x^9 + 2*x^7 + 2*x^5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lx^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx^17 + x^15 + x^13 + 2*x^9 + 2*x^7 + 2*x^5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3 - (x^17 + x^15 + x^13 + 2*x^9 + 2*x^7 + 2*x^5)

[?7h[?12l[?25h[?2004l[?7h2*x^13 + 2*x^5 + 2*x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l2*13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h2*x*t^4 + 2*x^2*t^3 + 2*x*t^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1
Crys of C:
( [0] d[x] + [1] d[y] + V((x^5 + x^3 + 2*x^2 + 2) dy) + dV(0), V(((x^2 + 2*x + 1)/x)*y) )
( [0] d[x] + [x] d[y] + V((x^8 + 2*x^6 + x^5 + 2*x^3 + x^2 + x + 1) dy) + dV(0), [2/x*y] + V(((x^5 + 2*x^4 + x^3 + x^2 + 2*x + 2)/x)*y) )

Crys of C1:
( [0] d[x] + [2] d[y] + V((2*x^3 + 2*x + 2) dy) + dV(0), V(((x^6 + x^4 + x^3 + 2)/x^3)*y) )
( [0] d[x] + [2*x] d[y] + V((2*x^14 + 2*x^12 + 2*x^11 + 2*x^6 + 2*x^4 + 2*x^3 + x^2) dy) + dV(0), V(((x^10 + x^8 + x^7 + 2*x^4 + x^2 + x + 2)/x^4)*y) )
( [0] d[x] + [2*x^2] d[y] + V((x^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) dy) + dV(0), V(((x^11 + x^9 + x^8 + 2*x^5 + x^3 + x^2 + 2*x + 1)/x^2)*y) )
( [0] d[x] + [2*x^3] d[y] + V((2*x^12 + 2*x^10 + 2*x^9 + x^8 + x^6 + 2*x^4 + 2*x^3 + x + 1) dy) + dV(0), V(((x^16 + x^14 + x^13 + 2*x^10 + x^8 + x^7 + 2*x^6 + x^5 + x^2 + x + 1)/x^4)*y) )
( [0] d[x] + [2*x^7 + 2*x] d[y] + V((2*x^32 + 2*x^30 + 2*x^29 + 2*x^24 + 2*x^22 + 2*x^21 + x^20 + 2*x^17 + x^16 + 2*x^14 + x^13 + x^12 + 2*x^11 + x^10 + x^8 + 2*x^7 + 2*x^5 + x^4 + x^3 + x + 1) dy) + dV(0), [2/x*y] + V(((x^28 + x^26 + x^25 + 2*x^22 + x^20 + x^19 + 2*x^18 + x^17 + x^14 + x^13 + x^12 + 2*x^11 + 2*x^10 + x^9 + 2*x^8 + 2*x^7 + 2*x^6 + x^5 + x^4 + x^3 + 2*x^2 + 2*x + 2)/x^4)*y) )
( [0] d[x] + [x^6 + 1] d[y] + V((x^21 + x^19 + x^18 + 2*x^17 + 2*x^15 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + 2*x^4 + x^3 + x) dy) + dV(0), [2/x^2*y] + V(((2*x^25 + 2*x^23 + 2*x^22 + x^19 + 2*x^17 + 2*x^16 + x^15 + 2*x^14 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + 2*x^6 + x^5 + x^4 + x^3 + 2*x^2 + 2)/x^4)*y) )
( [0] d[x] + [0] d[y] + V((2*x^8 + x^2 + 1) dy) + dV(0), [2/x^3*y] )
( [0] d[x] + [2*x^4] d[y] + V((2*x^23 + 2*x^21 + 2*x^20 + 2*x^15 + 2*x^13 + 2*x^12 + x^11 + 2*x^8 + x^7 + 2*x^5 + x^4 + 2*x^3 + x) dy) + dV(0), [2/x^4*y] + V(((x^19 + x^17 + x^16 + 2*x^13 + x^11 + x^10 + 2*x^9 + x^8 + x^5 + x^4 + x^3 + 2*x^2 + x + 1)/x^4)*y) )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^17 + x^15 + 2*x^9 + 2*x^7 + x^5 + 2*x^3).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lx^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: (x^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) - x^2 * 1

[?7h[?12l[?25h[?2004l[?7hx^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = G1.irreducible_characters()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: X = x^3 - x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX = x^3 - x[?7h[?12l[?25h[?25l[?7l(x^17 +x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) - x^2 * 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx^5 + x^3 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 2)[?7h[?12l[?25h[?25l[?7lX^2 + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7lX^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^5 + X^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7lX^5 + X^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^17 + x^15 + x^14 + 2*x^9 + 2*x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + 1) - x^2 * (X^5 + X^3 + 2*X^2 + 2)

[?7h[?12l[?25h[?2004l[?7hx^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(2*x^13 + 2*x^5 + 2*x^3, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lx^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(x^2 + 2*x + 1)*t^4 + (2*x^2 + x)*t^3 + (2*x^2 + 2*x + 1)*t^2 + x*t + 2*x^2 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lclass test:[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lclass test:[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.z[1]*C.x^i*C.dx + C.x^(M - m + i)*C.z[0]*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = crys[0].regular_form()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = crys[0].regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lsage: om.valuation()

  om.capitalize   om.encode       om.format       om.isalpha      om.isidentifier om.isspace      om.ljust        om.partition    om.rfind        om.rsplit       om.startswith   
 

  om.casefold     om.endswith     om.format_map   om.isascii      om.islower      om.istitle      om.lower        om.removeprefix om.rindex       om.rstrip       om.strip        
 

  om.center       om.expandtabs   om.index        om.isdecimal    om.isnumeric    om.isupper      om.lstrip       om.removesuffix om.rjust        om.split        om.swapcase     
>

  om.count        om.find         om.isalnum      om.isdigit      om.isprintable  om.join         om.maketrans    om.replace      om.rpartition   om.splitlines   om.title        
 

 [?7h[?12l[?25h[?25l[?7lcapitalize

 om.capitalize  







 <unknown> [?7h[?12l[?25h[?25l[?7lencode

 om.capitalize   om.encode      [?7h[?12l[?25h[?25l[?7lformat

 om.encode       om.format      [?7h[?12l[?25h[?25l[?7lisalpha

 om.format       om.isalpha     [?7h[?12l[?25h[?25l[?7lidentifier

 om.isalpha      om.isidentifier[?7h[?12l[?25h[?25l[?7lspace

 om.isidentifier om.isspace     [?7h[?12l[?25h[?25l[?7lljust

 om.isspace      om.ljust       [?7h[?12l[?25h[?25l[?7lpartition

 om.ljust        om.partition   [?7h[?12l[?25h[?25l[?7lrfind

 om.partition    om.rfind       [?7h[?12l[?25h[?25l[?7lsplit

 om.rfind        om.rsplit      [?7h[?12l[?25h[?25l[?7lstartswith

 om.rsplit       om.startswith  [?7h[?12l[?25h[?25l[?7ltrnslate

 encode    formatisalphaidentifierspace     ljust  partitionrfind    splitstartswithtrnslate  

 endswithformat_mapisascii   lowertitlelower  removeprefixindex      stripstrip upper 

<expandtabsindex     scimalnumericupp  ltrip removesuffixjust       spliwapcasezfill    

 find isalnumdigitprinablejoin       maketransreplace  partitionslilinestitle                      
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstrtswith

 om.startswith   om.translate   [?7h[?12l[?25h[?25l[?7lrsplit

 om.rsplit       om.startswith  [?7h[?12l[?25h[?25l[?7lfind

 om.rfind        om.rsplit      [?7h[?12l[?25h[?25l[?7lpartition

 om.partition    om.rfind       [?7h[?12l[?25h[?25l[?7lljust

 om.ljust        om.partition   [?7h[?12l[?25h[?25l[?7lisspace

 om.isspace      om.ljust       [?7h[?12l[?25h[?25l[?7lidentifier

 om.isidentifier om.isspace     [?7h[?12l[?25h[?25l[?7lalpha

 om.isalpha      om.isidentifier[?7h[?12l[?25h[?25l[?7lformat

 om.format       om.isalpha     [?7h[?12l[?25h[?25l[?7lencode

 om.encode       om.format      [?7h[?12l[?25h[?25l[?7lcapitalize

 capitalizeencodeformat alpha     identifierisspaceljust    partitionfind rsplit    strtswith 

 casefoldendswith  format_mapasciiloweristitlelower       emoveprefixindexrstripstrip 

 center    expandtabsnx    decimalnumiciupperlstrip      emovesuffixrjusplit   swapcase>

 countfind   alnumdigi    isprintablejoin     maketranseplace   raritionsplitlines om.title        
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









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[?7h[?12l[?25h[?2004l[?7h'( [0] d[x] + [1] d[y] + V((x^5 + x^3 + 2*x^2 + 2) dy) + dV(0), V(((x^2 + 2*x + 1)/x)*y) )'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lclass test:[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(crys1[2][?7h[?12l[?25h[?25l[?7l-crys1[2][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-crys1[2]).regular_form()

[?7h[?12l[?25h[?2004l[?7h'( [0] d[x] + [x^2] d[y] + V((2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2) dy) + dV(0), V(((2*x^11 + 2*x^9 + 2*x^8 + x^5 + 2*x^3 + 2*x^2 + x + 2)/x^2)*y) )'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l=2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 - x^6*(X^5+X^3 + 2*X^2 + 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = 2*x^17 + 2*x^15 + 2*x^14 + x^9 + x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 - x^6*(X^5+X^3 + 2*X^2 + 2)[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h2*x^21 + 2*x^19 + x^17 + 2*x^15 + 2*x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + x^3 + 2*x^2 + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor n in range(n0 + 1, 30):[?7h[?12l[?25h[?25l[?7lsage: f

[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: A/f

[?7h[?12l[?25h[?2004l[?7h(2*x^21 + 2*x^19 + x^17 + 2*x^15 + 2*x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + x^3 + 2*x^2 + 2)/(x^3 + 2*x + 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l.nth_root(p)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA/f[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.quo_rem(f)

[?7h[?12l[?25h[?2004l[?7h(2*x^18 + x^16 + x^15 + 2*x^14 + x^10 + x^9 + 2*x^8 + x^7 + 2*x^3 + 2*x^2 + 2*x + 1,
 2*x^2 + 2*x + 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(x^14 + 2*x^13 + x^8 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l, f)[?7h[?12l[?25h[?25l[?7l(, f)[?7h[?12l[?25h[?25l[?7lA, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(A, f)

[?7h[?12l[?25h[?2004l[?7h2*t^7 + (x + 1)*t^6 + (x^2 + 2)*t^5 + (2*x + 1)*t^4 + x^2*t^3 + (2*x^2 + x + 1)*t^2 + 2*x^2 + 2*x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega.cartier()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = a*omega[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: omega = C1.x^2*C1.dy

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [25], line 1
----> 1 omega = C1.x**Integer(2)*C1.dy

AttributeError: 'superelliptic' object has no attribute 'dy'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C1.x^2*C1.dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega = C1.x^2*C1.y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C1.x^2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega

[?7h[?12l[?25h[?2004l[?7h((-x^2)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift_form0(omega)

[?7h[?12l[?25h[?2004l[?7h[(2*x^2/(x^9 + x^3 + x + 1))*y] d[x] + V(((-x^35 - x^33 - x^32 + x^29 - x^26 - x^25 - x^23 - x^20 + x^19 + x^16 + x^15 - x^13 + x^10 - x^9 + x^8 - x^7 - x^6)/(x^18*y - x^12*y - x^10*y - x^9*y + x^6*y - x^4*y - x^3*y + x^2*y - x*y + y)) dx) + dV([((2*x^27 + 2*x^25 + 2*x^24 + 2*x^21 + x^19 + x^18 + 2*x^17 + x^16 + 2*x^15 + 2*x^13 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + 2*x^7)/(x^18 + 2*x^12 + 2*x^10 + 2*x^9 + x^6 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift_form0(omega).regular_form()

[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x^2] d[y] + V((0) dy) + dV(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega).regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(omega)[?7h[?12l[?25h[?25l[?7l8(omega)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7l = C1.x^2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ldy[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(A, f)[?7h[?12l[?25h[?25l[?7lomega = C1.x^2*C1.dy[?7h[?12l[?25h[?25l[?7ly.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift_form0(omega).regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ p = 3

m = 2

F = GF(p)

Rx.<x> = PolynomialRing(F)

f = x^3 - x

C = superelliptic(f, m)
bash: p: command not found
bash: m: command not found
bash: syntax error near unexpected token `('
bash: syntax error near unexpected token `('
bash: f: command not found
bash: syntax error near unexpected token `('
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: p = 3

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: f = x^3 - x

....: C = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7lsage: p = 3

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: f = x^3 - x

....: C = superelliptic(f, m)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [1], line 6
      4 Rx = PolynomialRing(F, names=('x',)); (x,) = Rx._first_ngens(1)
      5 f = x**Integer(3) - x
----> 6 C = superelliptic(f, m)

NameError: name 'superelliptic' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: p = 3

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: f = x^3 - x

....: C = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7lsage: p = 3

....: m = 2

....: F = GF(p)

....: Rx.<x> = PolynomialRing(F)

....: f = x^3 - x

....: C = superelliptic(f, m)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lx_series[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: C.x_series

[?7h[?12l[?25h[?2004l[?7h[t^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lafty/[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [6], line 1
----> 1 at_most_poles_superelliptic(Integer(3))

TypeError: at_most_poles_superelliptic() missing 1 required positional argument: 'pole_order'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC3)[?7h[?12l[?25h[?25l[?7l,3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [7], line 1
----> 1 at_most_poles_superelliptic(C,Integer(3))

File <string>:17, in at_most_poles_superelliptic(self, pole_order, threshold)

AttributeError: 'superelliptic' object has no attribute 'height'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lC,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [9], line 1
----> 1 at_most_poles_superelliptic(C,Integer(3))

File <string>:17, in at_most_poles_superelliptic(self, pole_order, threshold)

AttributeError: 'superelliptic' object has no attribute 'prec'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [11], line 1
----> 1 at_most_poles_superelliptic(C,Integer(3))

File <string>:17, in at_most_poles_superelliptic(self, pole_order, threshold, prec)

AttributeError: 'superelliptic' object has no attribute 'quotient'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [13], line 1
----> 1 at_most_poles_superelliptic(C,Integer(3))

File <string>:26, in at_most_poles_superelliptic(self, pole_order, threshold, prec)

TypeError: 'function' object cannot be interpreted as an integer
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [15], line 1
----> 1 at_most_poles_superelliptic(C,Integer(3))

File <string>:32, in at_most_poles_superelliptic(self, pole_order, threshold, prec)

File <string>:219, in holomorphic_combinations_fcts(S, pole_order)

AttributeError: 'superelliptic' object has no attribute 'prec'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [17], line 1
----> 1 at_most_poles_superelliptic(C,Integer(3))

File <string>:32, in at_most_poles_superelliptic(self, pole_order, threshold, prec)

File <string>:238, in holomorphic_combinations_fcts(S, pole_order)

File <string>:6, in __init__(self, C, g)

AttributeError: 'superelliptic' object has no attribute 'height'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [19], line 1
----> 1 at_most_poles_superelliptic(C,Integer(3))

File <string>:32, in at_most_poles_superelliptic(self, pole_order, threshold, prec)

File <string>:64, in holomorphic_combinations_fct_superelliptic(S, pole_order)

File <string>:6, in __init__(self, C, g)

AttributeError: 'superelliptic' object has no attribute 'height'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft7.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l[?7h[1, y, x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.quo_rem(f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.quo_rem(f)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7ly,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7lx][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y, C.x])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 with the equations:
z0^3 - z0 = y
z1^3 - z1 = x

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[x*z0^2*z1^2 + x^2*z1^2 + y*z0*z1^2,
 x^2*z0*z1^2 + y*z0^2*z1^2 + x*y*z1^2,
 x^2*z0^2*z1^2 + x^3*z1^2 + x*y*z0*z1^2,
 x^3*z0*z1^2 + x*y*z0^2*z1^2 + x^2*y*z1^2,
 x^3*z0^2*z1^2 + x^4*z1^2 + x^2*y*z0*z1^2,
 x^4*z0*z1^2 + x^2*y*z0^2*z1^2 + x^3*y*z1^2,
 x^4*z0^2*z1^2 + x^5*z1^2 + x^3*y*z0*z1^2,
 x^5*z0*z1^2 + x^3*y*z0^2*z1^2 + x^4*y*z1^2,
 x^5*z0^2*z1^2 + x^6*z1^2 + x^4*y*z0*z1^2,
 x^6*z0*z1^2 + x^4*y*z0^2*z1^2 + x^5*y*z1^2,
 x^6*z0^2*z1^2 + x^7*z1^2 + x^5*y*z0*z1^2,
 x^7*z0*z1^2 + x^5*y*z0^2*z1^2 + x^6*y*z1^2,
 x^7*z0^2*z1^2 + x^8*z1^2 + x^6*y*z0*z1^2,
 x^8*z0*z1^2 + x^6*y*z0^2*z1^2 + x^7*y*z1^2,
 x^8*z0^2*z1^2 + x^9*z1^2 + x^7*y*z0*z1^2,
 x^9*z0*z1^2 + x^7*y*z0^2*z1^2 + x^8*y*z1^2,
 x^9*z0^2*z1^2 + x^10*z1^2 + x^8*y*z0*z1^2,
 x^10*z0*z1^2 + x^8*y*z0^2*z1^2 + x^9*y*z1^2,
 x^10*z0^2*z1^2 + x^11*z1^2 + x^9*y*z0*z1^2,
 x^11*z0*z1^2 + x^9*y*z0^2*z1^2 + x^10*y*z1^2,
 x^11*z0^2*z1^2 + x^12*z1^2 + x^10*y*z0*z1^2,
 x^12*z0*z1^2 + x^10*y*z0^2*z1^2 + x^11*y*z1^2,
 x^12*z0^2*z1^2 + x^13*z1^2 + x^11*y*z0*z1^2,
 x^13*z0*z1^2 + x^11*y*z0^2*z1^2 + x^12*y*z1^2,
 x^13*z0^2*z1^2 + x^14*z1^2 + x^12*y*z0*z1^2,
 x^14*z0*z1^2 + x^12*y*z0^2*z1^2 + x^13*y*z1^2,
 x^14*z0^2*z1^2 + x^15*z1^2 + x^13*y*z0*z1^2,
 x^15*z0*z1^2 + x^13*y*z0^2*z1^2 + x^14*y*z1^2,
 x^15*z0^2*z1^2 + x^16*z1^2 + x^14*y*z0*z1^2,
 x^16*z0*z1^2 + x^14*y*z0^2*z1^2 + x^15*y*z1^2,
 x^16*z0^2*z1^2 + x^17*z1^2 + x^15*y*z0*z1^2,
 x^17*z0*z1^2 + x^15*y*z0^2*z1^2 + x^16*y*z1^2,
 x^17*z0^2*z1^2 + x^18*z1^2 + x^16*y*z0*z1^2,
 x^18*z0*z1^2 + x^16*y*z0^2*z1^2 + x^17*y*z1^2,
 x^18*z0^2*z1^2 + x^19*z1^2 + x^17*y*z0*z1^2,
 x^19*z0*z1^2 + x^17*y*z0^2*z1^2 + x^18*y*z1^2,
 x^19*z0^2*z1^2 + x^20*z1^2 + x^18*y*z0*z1^2,
 x^20*z0*z1^2 + x^18*y*z0^2*z1^2 + x^19*y*z1^2,
 x^20*z0^2*z1^2 + x^21*z1^2 + x^19*y*z0*z1^2,
 x^21*z0*z1^2 + x^19*y*z0^2*z1^2 + x^20*y*z1^2,
 x^21*z0^2*z1^2 + x^22*z1^2 + x^20*y*z0*z1^2,
 x^22*z0*z1^2 + x^20*y*z0^2*z1^2 + x^21*y*z1^2,
 x^22*z0^2*z1^2 + x^23*z1^2 + x^21*y*z0*z1^2,
 x^23*z0*z1^2 + x^21*y*z0^2*z1^2 + x^22*y*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzAS.magical_element()[?7h[?12l[?25h[?25l[?7l AS.magical_element()[?7h[?12l[?25h[?25l[?7l=AS.magical_element()[?7h[?12l[?25h[?25l[?7l AS.magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z = AS.magical_element()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z.trace()

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.trace()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z.valuation()

[?7h[?12l[?25h[?2004l[?7h+Infinity
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.valuation()[?7h[?12l[?25h[?25l[?7lsage: z

[?7h[?12l[?25h[?2004l[?7hx*z0^2*z1^2 + x^2*z1^2 + y*z0*z1^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z.valuation(prec = 200)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [29], line 1
----> 1 z.valuation(prec = Integer(200))

TypeError: as_function.valuation() got an unexpected keyword argument 'prec'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.valuation(prec = 200)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7ltrace()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7lAS.magicl_elemnt()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y, C.x])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y, C.x], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz.valuation(prec = 200)[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lAS.magical_element()[0][?7h[?12l[?25h[?25l[?7lsage: z = AS.magical_element()[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In [31], line 1
----> 1 z = AS.magical_element()[Integer(0)]

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_lement()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_lement()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h12
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.

  AS.a_number                            AS.branch_points                        

  AS.at_most_poles                       AS.cartier_matrix                       

  AS.at_most_poles_forms                 AS.characteristic                      >

  AS.base_ring                           AS.cohomology_of_structure_sheaf_basis  

 [?7h[?12l[?25h[?25l[?7la_number

 AS.a_number                           







 <unknown> [?7h[?12l[?25h[?25l[?7lbranch_points

 AS.a_number                            AS.branch_points                      [?7h[?12l[?25h[?25l[?7lde_rham_basi

 branch_pointsde_rham_basi

 cartiermatrixdx            

<characeristic     dx_seris     

 cohomoloy_of_structure_sheaf_basisexpnent_of_different              [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim

de_rham_basiexponent_of_different_prim

dx            fct_field

dx_seris     function

expnent_of_different              genus                [?7h[?12l[?25h[?25l[?7lgroup

exponent_of_different_primgroup                     

fct_fieldheight   

functionholomorphic_differentials_basis

genus                ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps

group                     jumps

height   lift_o_de_rham

holomorphic_differentials_basismagical_element                

ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7llift_to_de_rham

 AS.jumps                              

 AS.lift_to_de_rham                    [?7h[?12l[?25h[?25l[?7lheigh



 AS.height                              AS.lift_to_de_rham                    [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis



 AS.height                             

 AS.holomorphic_differentials_basis    [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx,
 ((x*z0^2 + x^2 + y*z0 - x*z1)/y) * dx,
 (1/y) * dx,
 (z1/y) * dx,
 (z1^2/y) * dx,
 (z0/y) * dx,
 (z0*z1/y) * dx,
 (z0*z1^2/y) * dx,
 (z0^2/y) * dx,
 ((z0^2*z1 - x*z1)/y) * dx,
 ((z0^2*z1^2 - x*z1^2 + x*z1)/y) * dx,
 (x/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft7.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(it.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l[?7h[1, x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7lz = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lz.valuatin(prec= 200)[?7h[?12l[?25h[?25l[?7lAS = as_cver(C,[C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y, C.x], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (x/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z1^2) * dx,
 (z0) * dx,
 ((x^3*z1^2 + x^2*z0^2 + y*z0*z1)/y) * dx,
 (1/y) * dx,
 (z1/y) * dx,
 (z1^2/y) * dx,
 (z0/y) * dx,
 (z0*z1/y) * dx,
 (z0*z1^2/y) * dx,
 (z0^2/y) * dx,
 (z0^2*z1/y) * dx,
 (z0^2*z1^2/y) * dx,
 ((-x^2*z0*z1^2 + x*y)/y) * dx,
 (x/y) * dx,
 (x*z1/y) * dx,
 (x*z1^2/y) * dx,
 (x*z0/y) * dx,
 (x*z0*z1/y) * dx,
 (x*z0*z1^2/y) * dx,
 (x*z0^2/y) * dx,
 (x*z0^2*z1/y) * dx,
 (x*z0^2*z1^2/y) * dx,
 (x^2/y) * dx,
 (x^2*z1/y) * dx,
 (x^2*z1^2/y) * dx,
 (x^2*z0/y) * dx,
 (x^2*z0*z1/y) * dx,
 (x^3/y) * dx,
 (x^3*z1/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

  AS.a_number                            AS.branch_points                        

  AS.at_most_poles                       AS.cartier_matrix                       

  AS.at_most_poles_forms                 AS.characteristic                      >

  AS.base_ring                           AS.cohomology_of_structure_sheaf_basis  

 [?7h[?12l[?25h[?25l[?7la_number

 AS.a_number                           







 <unknown> [?7h[?12l[?25h[?25l[?7lbranch_points

 AS.a_number                            AS.branch_points                      [?7h[?12l[?25h[?25l[?7lde_rham_basi

 branch_pointsde_rham_basi

 cartiermatrixdx            

<characeristic     dx_seris     

 cohomoloy_of_structure_sheaf_basisexpnent_of_different              [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim

de_rham_basiexponent_of_different_prim

dx            fct_field

dx_seris     function

expnent_of_different              genus                [?7h[?12l[?25h[?25l[?7lgroup

exponent_of_different_primgroup                     

fct_fieldheight   

functionholomorphic_differentials_basis

genus                ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps

group                     jumps

height   lift_o_de_rham

holomorphic_differentials_basismagical_element                

ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lone

jumpsone  

lift_o_de_rhamprec           

magical_element                pseudo_magical_element

nb_of_pts_at_nfty quotien          [?7h[?12l[?25h[?25l[?7lramification_jumps

one  ramification_jumps

prec           uniformizer

pseudo_magical_elementx                     

quotien          x_series[?7h[?12l[?25h[?25l[?7lone

 AS.one                                 AS.ramification_jumps                 [?7h[?12l[?25h[?25l[?7lprc

 AS.one                                

 AS.prec                               [?7h[?12l[?25h[?25l[?7lsudo_magical_element



 AS.prec                               

 AS.pseudo_magical_element             [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element()

[?7h[?12l[?25h[?2004l[?7h[z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,6)

[?7h[?12l[?25h[?2004l[?7h[1, y, x, x^2, x^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,6)[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_elemen()[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l = as_covr(C, [C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7lx, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l^, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l2, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x^2, C.x], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element()

[?7h[?12l[?25h[?2004l[?7h[z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lat_mostpls_superelliptic(C6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l9)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,9)

[?7h[?12l[?25h[?2004l[?7h[1, y, x, x*y, x^2, x^2*y, x^3, x^4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_elemen()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^2, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l*, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l., C.x], prec = 20)[?7h[?12l[?25h[?25l[?7ly, C.x], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y, C.x], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element()

[?7h[?12l[?25h[?2004l[?7h[z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lat_mostpls_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7lAS = ascvr(C, [C.x*C.y, C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7l.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7lC.x], prec = 20)[?7h[?12l[?25h[?25l[?7l.x], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element()

[?7h[?12l[?25h[?2004l[?7h[z0^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l^], prec = 20)[?7h[?12l[?25h[?25l[?7l3], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x^3], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x^3], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element()

[?7h[?12l[?25h[?2004l[?7h[x^2 + x*z0 + z0^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^3], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l4], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x^4], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x^4], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element()

[?7h[?12l[?25h[?2004l[?7h[z0^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,9)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,12)

[?7h[?12l[?25h[?2004l[?7h[1, y, x, x*y, x^2, x^2*y, x^3, x^3*y, x^4, x^5, x^6]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx_series[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.valuation()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [55], line 1
----> 1 C.x.valuation()

AttributeError: 'superelliptic_function' object has no attribute 'valuation'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion

 C.x.expansion         

 C.x.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 C.x.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 C.x.expansion         

 C.x.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^6 + 2*t^30 + t^54 + 2*t^78 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^3 + t^11 + t^27 + t^35 + 2*t^51 + t^75 + 2*t^83 + O(t^95)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,12)[?7h[?12l[?25h[?25l[?7lt_most_poles_superelliptic(C,12)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,5)

[?7h[?12l[?25h[?2004l[?7h[1, y, x, x^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x^4], prec = 200)[?7h[?12l[?25h[?25l[?7l= as_cover(C, [C.x^4], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l], prec = 20)[?7h[?12l[?25h[?25l[?7l,], prec = 20)[?7h[?12l[?25h[?25l[?7l ], prec = 20)[?7h[?12l[?25h[?25l[?7lC], prec = 20)[?7h[?12l[?25h[?25l[?7l.], prec = 20)[?7h[?12l[?25h[?25l[?7ly], prec = 20)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x, C.y], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x, C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lpseudo_magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element()

[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphicdifferentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (x/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lpseudo_magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 15)

[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 15)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30)

[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[((-x^2*z1 + y)/y) * dx,
 ((2*x^2*z1^2 + 2*x^3 + y*z1)/y) * dx,
 ((-2*x^2*z1^3 - x^3*z1 + y*z1^2 + 2*x*y)/y) * dx,
 ((x^2*z1^4 + x^3*z1^2 + x^4 - x^2*z0^2 + y*z1^3 + x*y*z1)/y) * dx,
 ((-x^2*z0*z1 + y*z0)/y) * dx,
 ((2*x^2*z0*z1^2 + 2*x^3*z0 - 2*x^2*z0^2 + y*z0*z1)/y) * dx,
 ((-2*x^2*z0*z1^3 - 2*x*z0^2*z1^3 - x^3*z0*z1 + 2*x^2*z0^2*z1 + y*z0*z1^2 + 2*x*y*z0 + x^2*z1)/y) * dx,
 ((x^2*z0*z1^4 + x*z0^2*z1^4 + x^3*z0*z1^2 - 2*x^2*z0^2*z1^2 + x^4*z0 + x^3*z0^2 + 2*x^2*z0^3 + y*z0*z1^3 + x*y*z0*z1 - x^2*z1^2 + x^3)/y) * dx,
 ((-2*x*z0^2*z1^3 + x^2*z0^2*z1 + y*z0^2)/y) * dx,
 ((2*x*z0^2*z1^4 - 2*x^2*z0^2*z1^2 - x^3*z0^2 + y*z0^2*z1)/y) * dx,
 ((-2*x*z0^3*z1^3 + x^2*z0^3*z1 + y*z0^3)/y) * dx,
 ((2*x*z0^3*z1^4 - 2*x^2*z0^3*z1^2 - x^3*z0^3 + y*z0^3*z1 + 2*x^2*z0^2)/y) * dx,
 ((-2*x*z0^4*z1^3 + x^2*z0^4*z1 + x*z0^2*z1^3 + y*z0^4 - x^2*z0^2*z1 - x^2*z1)/y) * dx,
 ((2*x*z0^4*z1^4 - 2*x^2*z0^4*z1^2 - x^3*z0^4 - x*z0^2*z1^4 + y*z0^4*z1 + 2*x^2*z0^2*z1^2 - x^3*z0^2 + 2*x^2*z0^3 + 2*x^2*z1^2 - 2*x^3)/y) * dx,
 (1/y) * dx,
 (z1/y) * dx,
 (z1^2/y) * dx,
 (z1^3/y) * dx,
 (z1^4/y) * dx,
 (z0/y) * dx,
 (z0*z1/y) * dx,
 (z0*z1^2/y) * dx,
 (z0*z1^3/y) * dx,
 (z0*z1^4/y) * dx,
 (z0^2/y) * dx,
 (z0^2*z1/y) * dx,
 (z0^2*z1^2/y) * dx,
 (z0^2*z1^3/y) * dx,
 ((z0^2*z1^4 - x^2*z0^2)/y) * dx,
 (z0^3/y) * dx,
 (z0^3*z1/y) * dx,
 (z0^3*z1^2/y) * dx,
 (z0^3*z1^3/y) * dx,
 ((z0^3*z1^4 - x^2*z0^3)/y) * dx,
 (z0^4/y) * dx,
 (z0^4*z1/y) * dx,
 (z0^4*z1^2/y) * dx,
 (z0^4*z1^3/y) * dx,
 ((z0^4*z1^4 - x^2*z0^4 + x^2*z0^2)/y) * dx,
 (x/y) * dx,
 (x*z1/y) * dx,
 (x*z1^2/y) * dx,
 ((x*z1^3 - x^2*z1)/y) * dx,
 ((x*z1^4 - 2*x^2*z1^2 + x^3)/y) * dx,
 (x*z0/y) * dx,
 (x*z0*z1/y) * dx,
 (x*z0*z1^2/y) * dx,
 ((x*z0*z1^3 - x^2*z0*z1)/y) * dx,
 ((x*z0*z1^4 - 2*x^2*z0*z1^2 + x^3*z0 + x^2*z0^2)/y) * dx,
 (x*z0^2/y) * dx,
 (x*z0^2*z1/y) * dx,
 ((x*z0^2*z1^2 - x^2*z0^2)/y) * dx,
 (x*z0^3/y) * dx,
 (x*z0^3*z1/y) * dx,
 ((x*z0^3*z1^2 - x^2*z0^3)/y) * dx,
 (x*z0^4/y) * dx,
 (x*z0^4*z1/y) * dx,
 ((x*z0^4*z1^2 - x^2*z0^4 - 2*x^2*z0^2)/y) * dx,
 (x^2/y) * dx,
 (x^2*z0/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h60
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 2[?7h[?12l[?25h[?25l[?7lagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: matrix

 matrix     

 matrix_plot





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(C); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(C); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7lS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In [67], line 1
----> 1 A, B = group_action_matrices_dR(AS)

File <string>:29, in group_action_matrices_dR(AS, threshold)

File <string>:345, in cohomology_of_structure_sheaf_basis(self, threshold)

File <string>:345, in <listcomp>(.0)

File <string>:131, in serre_duality_pairing(self, fct)

File /ext/sage/9.8/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
    583     return expression.sum(*args, **kwds)
    584 elif max(len(args),len(kwds)) <= 1:
--> 585     return sum(expression, *args, **kwds)
    586 else:
    587     from sage.symbolic.ring import SR

File <string>:131, in <genexpr>(.0)

File <string>:124, in residue(self, place)

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue()
    616         Integer Ring
    617     """
--> 618     return self[-1]
    619 
    620 def exponents(self):

File /ext/sage/9.8/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
    542         return type(self)(self._parent, f, self.__n)
    543 
--> 544     return self.__u[i - self.__n]
    545 
    546 def __iter__(self):

File /ext/sage/9.8/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
    451         return self.base_ring().zero()
    452     else:
--> 453         raise IndexError("coefficient not known")
    454 return self.__f[n]
    455 

IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 2[?7h[?12l[?25h[?25l[?7lagmathis(A1, A2)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A1, A2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 10 over GF(5),
RModule of dimension 25 over GF(5),
RModule of dimension 25 over GF(5)
]
{
[1 0 0 1 1 2 4 2 0 1]
[0 1 0 3 0 2 0 3 0 0]
[0 0 1 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 3 0 0 0]
[0 0 0 0 0 1 0 4 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 3]
[0 0 0 4 0 3 0 3 0 1],
[3 2 0 4 2 1 3 4 1 3]
[0 1 2 3 4 2 3 1 0 0]
[0 0 1 3 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 1 1 1 1 0 0]
[0 0 0 0 0 1 2 3 0 0]
[0 0 0 0 0 0 1 3 0 0]
[0 0 0 0 0 0 0 1 0 0]
[1 3 2 4 2 1 1 1 4 0]
[0 0 0 0 2 1 4 3 0 1]
}
{
[1 0 2 0 4 0 4 3 2 1 3 0 0 2 1 4 0 2 1 2 2 1 4 2 1]
[0 1 0 0 3 3 3 1 2 1 0 3 0 4 2 4 0 4 2 1 4 2 2 4 2]
[0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0]
[0 0 0 1 2 0 2 2 2 4 1 1 0 0 1 2 0 0 1 4 0 1 1 0 1]
[0 0 0 0 3 4 2 3 0 1 2 0 0 0 0 4 0 0 0 3 0 0 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 0 0]
[0 0 0 0 3 1 4 2 3 4 4 0 0 0 0 1 0 0 0 2 0 0 4 0 0]
[0 0 0 0 0 0 0 1 0 3 0 1 0 0 0 0 0 0 0 3 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 2 0 0 0 2 1 0 0 0 1 0 0 3 0 0 1 0 0]
[0 0 0 0 3 0 3 0 2 0 2 0 0 1 0 0 0 2 0 0 3 0 0 4 0]
[0 0 0 0 3 2 3 4 2 1 2 1 0 0 1 0 0 0 2 0 0 3 0 0 4]
[0 0 0 0 3 3 3 1 2 4 2 4 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 2 0 3 0 3 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1],
[1 2 3 3 4 0 2 2 2 4 0 2 3 1 1 1 1 2 2 0 0 0 0 0 0]
[0 1 3 3 3 1 0 1 3 4 4 3 4 0 0 0 0 2 2 0 0 0 0 0 0]
[0 0 1 0 4 0 4 0 0 2 3 0 0 4 4 4 4 1 1 0 0 0 0 0 0]
[0 0 0 1 0 1 3 1 0 2 3 4 4 1 1 1 1 2 2 0 0 0 0 0 0]
[0 0 0 0 3 1 2 1 2 4 3 1 1 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 1 0 1 3 1 2 4 3 0 0 0 0 0 3 3 0 0 0 0 0 0]
[0 0 0 0 3 2 4 0 3 1 2 4 4 0 0 0 0 4 4 0 0 0 0 0 0]
[0 0 0 0 2 3 2 2 2 4 3 1 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 2 3 2 1 2 4 3 1 1 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 1 3 1 1 3 1 3 4 0 1 2 3 4 0 0 0 0 0 0 0 0]
[0 0 0 0 2 3 2 1 3 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 4 0 3 4 4 1 3 0 0 0 0 0 1 2 0 0 0 0 0 0]
[0 0 0 0 2 3 2 1 3 4 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 2 1 1 2 0 0 0 0 0 0 0 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 3 2 2 0 0 0 0 0 0 0 0 1 2 0 0 0]
[0 0 0 0 0 0 0 0 2 1 4 2 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 2]
[0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1]
}
{
[1 0 0 0 1 0 0 1 1 2 3 4 0 0 0 0 0 1 0 2 1 3 1 0 4]
[0 1 0 0 0 1 1 1 1 3 3 0 2 1 0 0 0 0 0 1 4 0 1 3 4]
[0 0 1 0 0 0 3 1 2 2 0 0 2 2 0 0 0 2 0 0 3 0 4 1 0]
[0 0 0 1 0 0 2 3 2 4 3 1 3 1 0 0 0 0 0 3 0 2 1 0 1]
[0 0 0 0 1 0 1 0 3 0 2 0 3 0 0 0 0 0 0 0 0 0 4 2 0]
[0 0 0 0 0 1 4 3 4 3 1 2 1 3 0 0 0 0 0 1 0 4 1 0 2]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0]
[0 0 0 0 0 0 0 0 1 0 3 0 1 0 0 0 0 0 0 0 2 0 0 4 0]
[0 0 0 0 0 0 0 0 0 1 0 3 0 1 0 0 0 0 0 0 0 0 4 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 3 0 4 0 4 0 2 1 0 1 1 0 1 3 0 4 3 4]
[0 0 0 0 0 0 3 0 3 0 2 4 2 3 0 1 0 0 1 2 0 3 1 0 4]
[0 0 0 3 0 1 4 3 4 4 1 0 1 2 0 0 1 0 0 1 3 4 4 1 2]
[0 0 0 0 0 0 1 3 1 1 4 4 4 4 0 0 0 1 0 0 1 0 0 2 0]
[0 0 0 0 0 0 0 2 0 4 0 1 0 1 0 0 0 0 1 0 0 0 3 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 2 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1],
[1 1 1 1 0 0 0 4 0 3 2 4 4 0 0 0 0 0 2 4 3 3 0 0 0]
[0 1 2 3 0 0 4 2 4 4 2 4 1 1 0 3 0 2 4 2 0 0 0 0 0]
[0 0 1 3 0 0 2 1 2 2 1 1 2 3 0 3 0 0 0 2 1 1 0 0 0]
[0 0 0 1 0 0 3 0 3 0 2 2 0 3 0 0 0 2 4 4 3 3 0 0 0]
[0 0 0 0 1 1 1 1 0 0 4 4 4 4 0 0 0 2 1 2 1 1 0 0 0]
[0 0 0 0 0 1 4 1 2 1 4 3 1 0 0 0 0 4 3 0 4 4 0 0 0]
[0 0 0 0 0 0 3 4 2 2 3 3 3 3 0 0 0 0 0 2 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 4 4 2 0 0 0 0 0 0 0 3 3 0 0 0]
[0 0 0 0 0 0 3 4 4 4 2 2 2 2 0 0 0 0 0 3 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 3 3 4 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[4 2 3 1 1 3 2 3 4 0 1 0 0 4 1 3 0 4 0 0 3 3 0 0 0]
[0 0 0 0 0 0 2 0 2 0 2 2 2 2 0 1 0 3 1 1 0 0 0 0 0]
[0 0 0 0 4 2 0 3 2 4 4 0 0 3 0 0 1 0 4 4 2 2 0 0 0]
[0 0 0 0 0 0 4 2 4 4 1 1 1 1 0 0 0 1 4 4 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 3 0 0 0 0 0 1 0 2 2 0 0 0]
[0 0 0 0 0 0 4 1 4 2 0 2 3 3 0 0 0 0 0 1 3 3 0 0 0]
[0 0 0 0 0 0 0 0 0 0 2 2 4 4 0 0 0 0 0 0 1 2 0 0 0]
[0 0 0 0 0 0 0 0 0 0 4 2 3 4 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 1 2]
[0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: C1 = super

  super                          superelliptic_drw/             superelliptic_function          

  superelliptic                  superelliptic_drw_cech         superelliptic_regular_drw_form  

  superelliptic/                 superelliptic_drw_form         superelliptic_regular_form     >

  superelliptic_cech             superelliptic_form             superelliptic_witt              

 [?7h[?12l[?25h[?25l[?7l

 super                         







 <unknown> [?7h[?12l[?25h[?25l[?7lsuperelliptic

 super                         

 superelliptic                 [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(1, x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:2447, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
   2446 try:
-> 2447     right = Integer(right)
   2448 except TypeError:

File /ext/sage/9.8/src/sage/rings/integer.pyx:655, in sage.rings.integer.Integer.__init__()
    654 if otmp is not None:
--> 655     set_from_Integer(self, otmp(the_integer_ring))
    656     return

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:1396, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
   1395 if self.degree() > 0:
-> 1396     raise TypeError("cannot convert nonconstant polynomial")
   1397 return R(self.get_coeff_c(0))

TypeError: cannot convert nonconstant polynomial

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Cell In [70], line 1
----> 1 C1 = superelliptic(Integer(1), x)

File <string>:20, in __init__(self, f, m, prec)

File <string>:14, in __init__(self, C, g)

File <string>:260, in reduction(C, g)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:2449, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
   2447         right = Integer(right)
   2448     except TypeError:
-> 2449         raise TypeError("non-integral exponents not supported")
   2450 
   2451 d = self.degree()

TypeError: non-integral exponents not supported
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(1, x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(x, 1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lx.expansionat_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + t^6 + 2*t^14 + 4*t^30 + 2*t^38 + t^46 + t^70 + t^78 + 3*t^86 + 2*t^94 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^3 + 4*t^19 + 2*t^27 + 2*t^35 + 2*t^43 + 3*t^67 + t^75 + t^83 + O(t^95)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7lx][?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l([)][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l^][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7lC][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l.][?7h[?12l[?25h[?25l[?7lx][?7h[?12l[?25h[?25l[?7l^][?7h[?12l[?25h[?25l[?7l(][?7h[?12l[?25h[?25l[?7l-][?7h[?12l[?25h[?25l[?7l5][?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^(-5)])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^(-5)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^(-5)])[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holoAS[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1= group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1= group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1)

[?7h[?12l[?25h[?2004lIncrease precision.
Increase precision.
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [76], line 1
----> 1 A1, B1 = group_action_matrices_holo(AS1)

File <string>:20, in group_action_matrices_holo(AS)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:99, in coordinates(self, basis)

File <string>:16, in linear_representation_polynomials(polynomial, list_of_polynomials)

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^(-5)])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^(-5)], prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^(-5)], prec = 100)[?7h[?12l[?25h[?25l[?7l1,B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1)

[?7h[?12l[?25h[?2004lIncrease precision.
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [78], line 1
----> 1 A1, B1 = group_action_matrices_holo(AS1)

File <string>:20, in group_action_matrices_holo(AS)

File <string>:139, in holomorphic_differentials_basis(self, threshold)

File <string>:426, in holomorphic_combinations(S)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:78, in __rmul__(self, constant)

File <string>:10, in __init__(self, C, g)

File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:655, in PolynomialRing(base_ring, *args, **kwds)
    653 for arg in args:
    654     try:
--> 655         k = Integer(arg)
    656     except TypeError:
    657         # Interpret arg as names
    658         if names is not None:

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^(-5)], prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l], prec = 10)[?7h[?12l[?25h[?25l[?7l5], prec = 10)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 100)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 100)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 100)[?7h[?12l[?25h[?25l[?7l1,B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1)

[?7h[?12l[?25h[?2004lIncrease precision.
Increase precision.
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [80], line 1
----> 1 A1, B1 = group_action_matrices_holo(AS1)

File <string>:20, in group_action_matrices_holo(AS)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:99, in coordinates(self, basis)

File <string>:16, in linear_representation_polynomials(polynomial, list_of_polynomials)

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:905, in sage.matrix.matrix2.Matrix.solve_right()
    903 
    904         if not self.is_square():
--> 905             X = self._solve_right_general(C, check=check)
    906         else:
    907             try:

File /ext/sage/9.8/src/sage/matrix/matrix2.pyx:1028, in sage.matrix.matrix2.Matrix._solve_right_general()
   1026     # Have to check that we actually solved the equation.
   1027     if self*X != B:
-> 1028         raise ValueError("matrix equation has no solutions")
   1029 return X
   1030 

ValueError: matrix equation has no solutions
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^5], prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 300)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l1,B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7l, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1)

[?7h[?12l[?25h[?2004l[?7h[
RModule M of dimension 10 over GF(5)
]
{
[1 1 1 1 1 0 0 0 0 0]
[0 1 2 3 4 0 0 0 0 0]
[0 0 1 3 1 0 0 0 0 0]
[0 0 0 1 4 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 1 1 1 1]
[0 0 0 0 0 0 1 2 3 4]
[0 0 0 0 0 0 0 1 3 1]
[0 0 0 0 0 0 0 0 1 4]
[0 0 0 0 0 0 0 0 0 1],
[1 0 0 0 4 1 0 4 0 2]
[0 1 0 0 0 0 1 0 2 0]
[0 0 1 0 0 0 0 1 0 4]
[0 0 0 1 0 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0 1]
[0 0 0 0 3 1 0 3 0 1]
[0 0 0 0 0 0 1 0 4 0]
[0 0 0 0 0 0 0 1 0 3]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l





 









 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS1)[?7h[?12l[?25h[?25l[?7lS1= as_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l.genu()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lmification_jump[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps

[?7h[?12l[?25h[?2004l[?7h{0: [2, 1]}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 











 [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

























 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 























 [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 































 [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 































 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





























 [?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^5 + x + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

























 [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,5)

[?7h[?12l[?25h[?2004l[?7h[1, y, x, x^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





















 [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-5 + t^3 + t^5 + t^11 + 2*t^15 + t^23 + t^25 + t^27 + t^29 + 2*t^33 + t^35 + 2*t^45 + t^47 + 2*t^49 + t^51 + t^69 + 2*t^71 + t^75 + t^77 + t^83 + t^85 + 2*t^87 + 2*t^93 + O(t^95)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 















 [?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x, C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l= as_cover(C, [C.x, C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[C.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 













 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [90], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:7

File <string>:43, in __init__(self, f, m, prec)

TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-2 + t + t^2 + 2*t^5 + 2*t^6 + t^7 + t^8 + t^11 + 2*t^13 + t^15 + 2*t^18 + t^20 + 2*t^24 + t^25 + t^29 + 2*t^33 + t^35 + 2*t^37 + t^41 + 2*t^43 + t^45 + t^47 + t^49 + 2*t^54 + t^56 + 2*t^60 + 2*t^64 + t^68 + 2*t^72 + t^74 + t^76 + t^79 + t^80 + t^83 + 2*t^87 + t^89 + O(t^98)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_most_poles_superelliptic(C,5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C,3)

[?7h[?12l[?25h[?2004l[?7h[1, y, x, x*y, x^2, x^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.y).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-3 + 2 + 2*t + t^3 + 2*t^5 + 2*t^6 + 2*t^8 + t^13 + 2*t^17 + 2*t^20 + t^22 + 2*t^27 + 2*t^35 + t^37 + 2*t^39 + t^41 + t^47 + t^49 + t^53 + 2*t^56 + t^58 + t^60 + t^64 + 2*t^66 + t^68 + 2*t^72 + 2*t^74 + 2*t^78 + 2*t^81 + 2*t^87 + 2*t^89 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l.C.y], prec = 20)[?7h[?12l[?25h[?25l[?7lxC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l*C.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.jumps[?7h[?12l[?25h[?25l[?7lpseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7leudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [97], line 1
----> 1 AS.pseudo_magical_element(threshold = Integer(30))

File <string>:206, in pseudo_magical_element(self, threshold)

File <string>:192, in at_most_poles(self, pole_order, threshold)

File <string>:192, in <listcomp>(.0)

TypeError: as_function.expansion_at_infty() got an unexpected keyword argument 'place'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30)

[?7h[?12l[?25h[?2004l[?7h[-x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + y,
 x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + y*z0,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x*z0,
 -x^55 + x^53*z0^2 - x^54 + x^53*y - x^53*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*z0 + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 + x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*y - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^42*z0^2 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*z0 + x^40*z0^2 + x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*y*z0 + x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^33*z0^2 + x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^33 + x^32*z0 - x^31*z0^2 - x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^30*z0 - x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 - x^26*z0 + x*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x*y,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^51*y - x^51*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^45*y + x^44*y*z0 - x^44*y + x^44*z0 - x^43*y*z0 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 - x^36*z0^2 - x^36*z0 - x^35*y*z0 - x^36 + x^35*y + x^34*y*z0 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x^2,
 x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + x^2*z0,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + x^2*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^2*y,
 x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^44*y*z0^2 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^35*y*z0 - x^34*y*z0^2 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^26*y*z0 - x^26*y + x^26*z0 + x^2*y*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^51 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^49*z0 + x^47*y*z0^2 - x^49 + x^48*y + x^47*y*z0 + x^47*z0 - x^46*y*z0 - x^46*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*z0^2 + x^45 + x^44*z0 - x^42*y*z0^2 + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*y + x^41*z0 - x^40*z0^2 + x^41 - x^39*z0^2 - x^40 + x^38*z0^2 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^35*y*z0 + x^36 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^31*z0^2 - x^32 + x^30*z0^2 + x^29*y*z0^2 + x^31 - x^29*z0^2 + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^2*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^3,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^45 - x^44*z0 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*y + x^38*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*z0^2 - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^26*y + x^26*z0 + x^3*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^3*y,
 x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 - x^31*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^26*y - x^26*z0 + x^3*y*z0,
 x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^50*y*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*y - x^42*z0^2 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 + x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 - x^32 + x^31*z0 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 + x^26*z0 + x^3*y*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^4,
 -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 - x^27 - x^26*z0 + x^4*z0,
 x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 - x^51 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 - x^45*y*z0^2 - x^47 + x^45*z0^2 + x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^39 - x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^36*y*z0 + x^36*z0^2 + x^37 - x^35*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^33 + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^30 + x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^26*z0 + x^4*z0^2,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^27 + x^26*z0 + x^4*y,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 - x^52 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^31*y*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 - x^27 + x^26*y + x^26*z0 + x^4*y*z0,
 x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 - x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^39 - x^38*y + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^33*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^30 + x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^27*y*z0 - x^26*y*z0^2 + x^28 - x^26*z0^2 + x^26*y - x^26*z0 + x^4*y*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0 + x^39*z0^2 - x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y - x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^26*y*z0 - x^26*y + x^5*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*z0^2 + x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 - x^48*y + x^47*y*z0 + x^46*y*z0^2 - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^44 - x^43*y - x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^35 + x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 - x^33 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y + x^26*z0^2 - x^27 + x^5*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^5*y,
 -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^40*z0 - x^39*z0^2 + x^40 + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^31*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 - x^26*z0 + x^5*y*z0,
 -x^55 + x^53*z0^2 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^50*y*z0^2 - x^52 + x^50*y*z0 - x^50*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^45 + x^43*z0^2 - x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^35*z0 + x^34*y - x^34*z0 - x^33*y*z0 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y - x^31*z0^2 + x^32 + x^31*z0 + x^29*y*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^26*z0 + x^5*y*z0^2,
 x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^6,
 x^55 + x^54*z0 - x^54 - x^53*y - x^52*y*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^49*y*z0^2 + x^51 - x^50*y + x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48*z0 - x^47*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^47 - x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*z0 + x^40*y*z0^2 - x^42 - x^41*y + x^39*y*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0 + x^33 + x^32*y - x^30*y*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^29 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^6*y,
 -x^54*z0 - x^53*z0^2 - x^54 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27 - x^26*z0 + x^6*y*z0,
 -x^55 - x^54*z0 + x^53*y + x^52*y*z0 + x^52*z0^2 - x^50*y*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^48 - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y + x^46*z0 + x^45*z0^2 - x^45*z0 - x^44*y*z0 + x^45 + x^44*z0 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^41*z0^2 - x^41*y - x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^37*y + x^37*z0 + x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y + x^34*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^32*y + x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^28*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*y*z0^2,
 x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 + x^48*y*z0 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^48 + x^47*y + x^47*z0 + x^47 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^40*y*z0^2 + x^42 - x^41*z0 - x^40*z0^2 - x^41 + x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^33*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^31*y*z0^2 - x^33 + x^32*z0 + x^31*z0^2 + x^32 - x^30*z0^2 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^26*z0^2 + x^27 - x^26*z0 + x^7*z0^2,
 x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^46*y - x^46*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^7*y,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^51*y + x^51*z0 - x^49*y*z0^2 - x^50*y - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 - x^49 + x^48*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^46*y*z0 + x^46*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 - x^46 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 + x^42*y*z0^2 + x^42*y*z0 - x^42*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 + x^40*z0^2 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*y - x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^37*y - x^37 - x^36*y + x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y + x^35*z0 - x^33*y*z0^2 + x^35 - x^33*y*z0 - x^34 + x^33*y - x^32*y*z0 + x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*z0^2 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^28 - x^27*y + x^26*y - x^26*z0 + x^7*y*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^8,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^26*z0 + x^8*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^50 + x^48*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 + x^38 + x^36*y*z0 + x^36*z0^2 - x^37 - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^32*z0 - x^30*y*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^8*z0^2,
 x^54*z0 + x^53*z0^2 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^26*y + x^8*y*z0,
 x^55 - x^53*z0^2 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^50 + x^49*y + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^43*y + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y - x^33*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0 - x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0^2 + x^26*z0 + x^8*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^40*y*z0 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*z0^2 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*y*z0 - x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^26*z0 + x^9*z0,
 -x^54 + x^52*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 - x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*y - x^42*z0 - x^40*y*z0^2 - x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^35*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^31*y*z0^2 + x^33 - x^32*y + x^30*y*z0^2 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 + x^26*y + x^26*z0 + x^9*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*z0^2 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y + x^36*z0 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*z0^2 + x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^9*y*z0,
 x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y - x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^47*y*z0^2 + x^47*y*z0 + x^46*y*z0^2 + x^48 - x^46*z0^2 + x^47 - x^45*y*z0 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^37*y + x^37*z0 + x^35*y*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y + x^26*z0 + x^9*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^10,
 x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*y + x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*z0 + x^32*z0^2 - x^32*z0 + x^31*y*z0 + x^32 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 + x^26*y*z0 - x^26*z0 + x^10*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 - x^46 - x^44*y*z0 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 + x^41 - x^40 - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 - x^37 - x^36*y + x^36*z0 + x^35*z0^2 + x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y + x^32*z0 - x^32 + x^31 + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^10*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^42 + x^41*y - x^41 - x^39*z0^2 + x^39*z0 - x^38*z0^2 + x^39 + x^38*y - x^38*z0 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 + x^33 - x^32*y + x^31*z0^2 + x^32 - x^30*z0^2 - x^30*z0 + x^29*z0^2 - x^30 - x^29*y + x^29*z0 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^10*y*z0^2,
 x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27 - x^26*y - x^26*z0 + x^11,
 x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^26*y*z0 - x^26*y + x^11*z0,
 x^55 - x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 - x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^47 - x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 + x^36*y + x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^34 - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^11*z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*y + x^11*y,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0 + x^11*y*z0,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^47*y*z0^2 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^43*y*z0^2 + x^44*y + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^35*z0^2 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y - x^33*z0 - x^33 + x^32*y - x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*z0^2 + x^29 - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^11*y*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27 - x^26*y + x^26*z0 + x^12,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 - x^27 - x^26*y - x^26*z0 + x^12*z0,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 + x^52 + x^51*y + x^51*z0 + x^50*z0^2 + x^51 + x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 - x^44*y*z0 - x^44*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^39*y*z0^2 + x^41 - x^39*z0^2 + x^39*y - x^39*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^30*y*z0^2 - x^32 + x^30*z0^2 - x^30*y + x^30*z0 - x^29*z0^2 - x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^28*z0 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^12*z0^2,
 -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27 + x^26*z0 + x^12*y,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y - x^41 + x^40*z0 - x^39*z0^2 - x^40 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^12*y*z0,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 - x^50 + x^49 - x^48*y + x^48*z0 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^45*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^43*y*z0 + x^43*z0^2 - x^44 - x^43*z0 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 - x^38 - x^36*y*z0 + x^36*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^34*z0 + x^33*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 - x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^12*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^13,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^45*y*z0^2 - x^46*y + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 - x^36*y + x^35*y*z0 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*y,
 -x^54*z0 - x^53*z0^2 + x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^41 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y + x^28*z0^2 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^26*y + x^26*z0 + x^13*y*z0,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^51 - x^50*y + x^49*y*z0 + x^49*z0^2 - x^49*y - x^49*z0 + x^48*y*z0 - x^47*y*z0^2 + x^48*y + x^47*z0^2 - x^46*y*z0^2 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 + x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^27*y*z0^2 - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^13*y*z0^2,
 x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^14,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 + x^47*z0^2 - x^46*y*z0^2 + x^48 - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 - x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 - x^36*y + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^29*y*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^14*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^47*y*z0 - x^46*y*z0^2 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 - x^26*y + x^26*z0 + x^14*y,
 -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*z0 + x^46*y*z0^2 + x^48 - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^37*z0^2 - x^37*y + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^26*y*z0 - x^26*z0 + x^14*y*z0,
 x^55 + x^54*z0 - x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^50*y*z0 - x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^43*y*z0 + x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 + x^41*y - x^41*z0 + x^40*z0^2 + x^41 - x^40*z0 - x^38*y*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^34*y - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^26*y + x^14*y*z0^2,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 - x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^15,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^47*z0 - x^45*y*z0^2 + x^47 - x^46*z0 - x^45*y*z0 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^45 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*z0 - x^42*z0^2 - x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*y + x^41*z0 + x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^36*y*z0 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 - x^35*y*z0 - x^36 - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^31*y*z0^2 - x^32*y - x^32*z0 - x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*z0 - x^29*y*z0 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x^15*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^52 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^44*y*z0^2 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^40*z0 - x^39*y*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^15*y*z0,
 -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*y + x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 + x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 + x^32 + x^31*z0 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*z0 + x^15*y*z0^2,
 x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27 + x^26*y - x^26*z0 + x^16,
 x^55 - x^53*z0^2 + x^54 - x^53*y + x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 - x^50*y*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^51 - x^50*z0 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^48 - x^47*z0 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*z0^2 + x^45 - x^44*y - x^43*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^40*y*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^38*y*z0 - x^39 - x^38*y + x^38*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 + x^37*y - x^37*z0 + x^36*y*z0 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*z0^2 - x^35 - x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^31*y*z0^2 - x^33 + x^32*y + x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^29*y*z0 + x^28*y*z0^2 + x^30 + x^29*y - x^29*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*y - x^26*z0 + x^16*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^40*y*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*z0 + x^31*y*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^27 + x^16*y*z0,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^52*z0^2 - x^51*y*z0^2 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^49 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 + x^43*y*z0^2 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 - x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*y + x^36*y*z0 + x^36*z0^2 + x^37 - x^34*y*z0^2 - x^36 - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^16*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^17,
 x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 + x^53 + x^52 - x^51*y - x^51 + x^50*y + x^48*y*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^47 + x^46 - x^45 + x^42*y*z0^2 + x^42*y + x^41*y - x^39*y*z0^2 - x^41 + x^38*y*z0^2 + x^40 + x^36*y*z0^2 - x^38 + x^35*y*z0^2 + x^37 + x^36*y - x^36 + x^35 - x^33*y - x^32*y + x^32 - x^31 + x^29 - x^28 - x^27*y + x^26*z0^2 + x^27 + x^26*y + x^17*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27 - x^26*y + x^26*z0 + x^17*y,
 x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^50 + x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*z0 - x^42*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^42 + x^41*y - x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^34*z0 - x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^33 - x^32*y + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 + x^29*y*z0 - x^28*y*z0^2 - x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^17*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*y*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*z0^2 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*z0 + x^18*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y - x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 - x^47*z0 - x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*z0 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 + x^36*y*z0 + x^36*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 - x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^18*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^18*y,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^18*y*z0,
 x^54 - x^53*z0 - x^52*z0^2 + x^53 - x^52*y + x^51*y*z0 + x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^48 - x^47*y - x^46*y*z0 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 + x^44*y*z0 - x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^36 + x^34*y*z0 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 + x^31 - x^30*z0 + x^29*y + x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 - x^26*y + x^18*y*z0^2,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^26*y + x^26*z0 + x^19,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 + x^51 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 + x^40*y*z0^2 - x^42 - x^41*y - x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^38*y + x^37*y*z0 + x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^28*y*z0 + x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^19*z0^2,
 x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^19*y,
 x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 + x^40*z0 + x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*y*z0 + x^19*y*z0,
 x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^45*y*z0^2 + x^47 - x^46*y - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*y*z0 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^32 - x^31*z0 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^19*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^41*y*z0^2 + x^43 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 + x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^26*y*z0 - x^27 + x^26*y + x^20*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 - x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 + x^49*y*z0^2 + x^51 - x^50*y - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^46 + x^45*y + x^45*z0 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*z0^2 + x^44 - x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 - x^41*z0^2 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 - x^32*y*z0^2 - x^33*y + x^32*y*z0 + x^32*z0^2 - x^32*y - x^32*z0 + x^30*y*z0^2 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*z0^2 - x^27 + x^26*y + x^26*z0 + x^20*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y + x^48*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^32*z0^2 + x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^26*z0 + x^20*y*z0,
 -x^55 + x^53*z0^2 + x^53*y - x^53*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^40*z0^2 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*z0 + x^37*y*z0 + x^38 - x^37*z0 - x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^27 + x^26*y + x^20*y*z0^2,
 x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*y*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*z0^2 - x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^32*y*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y + x^32*z0 + x^31*y*z0 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y - x^26*z0 + x^21*z0,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 + x^45*y - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0^2 + x^39*z0^2 - x^39*y - x^39*z0 - x^38*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 + x^33 + x^32*y + x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 + x^29*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^26*y - x^26*z0 + x^21*z0^2,
 x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 - x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*y - x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^33 + x^32*y - x^32*z0 - x^31*z0^2 - x^30*z0^2 + x^31 + x^30*y - x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 - x^26*y - x^26*z0 + x^21*y*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*z0^2 + x^42 + x^41*y + x^40*y*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^22*z0,
 -x^55 + x^53*z0^2 + x^53*y + x^53*z0 + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^48*y*z0^2 - x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^37*y*z0 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^32*y*z0^2 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^28*y*z0 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^22*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^22*y,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^26*z0 + x^22*y*z0,
 x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^50 + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 - x^42*y + x^41*z0^2 + x^42 + x^40*z0^2 - x^41 + x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^38*y - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^34*z0 + x^32*y*z0^2 + x^34 + x^33*y + x^32*z0^2 - x^33 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*y + x^27*y*z0^2 + x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*z0 + x^22*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^52 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y - x^26*z0 + x^23,
 x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 - x^53 - x^51*z0^2 + x^52 + x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^23*z0,
 -x^55 - x^54*z0 + x^53*y + x^52*y*z0 - x^52*z0 - x^51*z0^2 - x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 + x^49 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y + x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27 - x^26*y + x^23*z0^2,
 x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 - x^40*z0 + x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^26*y*z0 + x^26*z0 + x^23*y*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*z0^2 - x^43 - x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 - x^40*z0^2 - x^40*z0 + x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*y + x^32*z0 + x^31*z0^2 + x^31*z0 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^23*y*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*z0 - x^40*y*z0 + x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^31*y*z0 - x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*z0 + x^24*z0,
 x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*z0 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 + x^44*y*z0^2 + x^45*y - x^43*y*z0^2 - x^44*y + x^44*z0 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 - x^41*y + x^41*z0 - x^39*y*z0^2 - x^41 + x^39*y - x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y - x^32*z0 + x^30*y*z0^2 + x^32 - x^30*y + x^29*z0^2 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*z0 + x^27*y*z0 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y - x^26*z0 + x^24*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^24*y,
 x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*z0^2 + x^52 - x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y + x^26*z0 + x^24*y*z0,
 -x^54 - x^53*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^47*y*z0^2 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^42 - x^41*z0 + x^40*z0^2 + x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^33 + x^32*z0 - x^31*z0^2 - x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^24*y*z0^2,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 - x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27 - x^26*z0 + x^25,
 x^55 + x^54*z0 + x^54 - x^53*y - x^53*z0 - x^52*y*z0 + x^52*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 - x^41 - x^39*z0^2 + x^39*y - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 - x^31*z0^2 + x^32 + x^30*z0^2 - x^30*y + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27 - x^26*y - x^26*z0 + x^25*z0^2,
 -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^50*y*z0^2 - x^51*y - x^50*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^47*y - x^45*y*z0^2 - x^47 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^41*y*z0 + x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*z0^2 - x^40*z0 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^36*y + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^32*y*z0 - x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0^2 + x^31*z0 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 + x^27*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^25*y*z0^2 - x^27 + x^26*y - x^26*z0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx,
 (1/y) * dx,
 (z0/y) * dx,
 ((-x^2 + z0^2)/y) * dx,
 (x/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.

  AS.a_number                            AS.branch_points                       AS.de_rham_basis                       
 

  AS.at_most_poles                       AS.cartier_matrix                      AS.dx                                  
 

  AS.at_most_poles_forms                 AS.characteristic                      AS.dx_series                           
>

  AS.base_ring                           AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different               
 

 [?7h[?12l[?25h[?25l[?7la_number

 AS.a_number                           







 <unknown> [?7h[?12l[?25h[?25l[?7lt_most_poles

 AS.a_number                           

 AS.at_most_poles                      [?7h[?12l[?25h[?25l[?7lcartiermatrix



 AS.at_most_poles                       AS.cartier_matrix                     [?7h[?12l[?25h[?25l[?7ldx



 AS.cartier_matrix                      AS.dx                                 [?7h[?12l[?25h[?25l[?7lfct_field

 branch_pointsde_rham_basiexponent_of_different_prim

 cartiermatrixdx            fct_field

<characeristic     dx_seris     function

 cohomoloy_of_structure_sheaf_basisexpnent_of_different              genus                [?7h[?12l[?25h[?25l[?7lheight

de_rham_basiexponent_of_different_primgroup                     

dx            fct_fieldheight   

dx_seris     functionholomorphic_differentials_basis

expnent_of_different              genus                ith_ramification_gp[?7h[?12l[?25h[?25l[?7llift_o_de_rham

exponent_of_different_primgroup                     jumps

fct_fieldheight   lift_o_de_rham

functionholomorphic_differentials_basismagical_element                

genus                ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lprec

group                     jumpsone  

height   lift_o_de_rhamprec           

holomorphic_differentials_basismagical_element                pseudo_magical_element

ith_ramification_gpnb_of_pts_at_nfty quotien          [?7h[?12l[?25h[?25l[?7luniformizer

jumpsone  ramification_jumps

lift_o_de_rhamprec           uniformizer

magical_element                pseudo_magical_elementx                     

nb_of_pts_at_nfty quotien          x_series[?7h[?12l[?25h[?25l[?7ly_series

one  ramification_jumpsy                  

prec           uniformizery_series    

pseudo_magical_elementx                     z 

quotien          x_seriesz 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7luniformizer



 AS.uniformizer                         AS.y_series                           [?7h[?12l[?25h[?25l[?7lprec



 AS.prec                                AS.uniformizer                        [?7h[?12l[?25h[?25l[?7llift_to_de_rham

jumpsone               ramification_jumps 

lift_to_de_rhamprec       uniformizer 

magical_element       pseudo_magical_elementx>

nb_of_ps_at_inftyquotientx 
[?7h[?12l[?25h[?25l[?7lheigh

groupjumpsone               

heigh         lift_to_de_rhamprec       

holomorphic_differentials_basismagical_element       pseudo_magical_element

ith_ramificaton_gpnb_of_ps_at_inftyquotient[?7h[?12l[?25h[?25l[?7lfct_field

exponent_of_different_primgroupjumps

fct_fieldheigh         lift_to_de_rham

functions                      holomorphic_differentials_basismagical_element       

genus              ith_ramificaton_gpnb_of_ps_at_infty[?7h[?12l[?25h[?25l[?7ldx

de_rham_basis             exponent_of_different_primgroup

dx       fct_fieldheigh         

dx_seriefunctions                      holomorphic_differentials_basis

exponent_of_differentgenus              ith_ramificaton_gp[?7h[?12l[?25h[?25l[?7lcartier_matrix

branch_pointde_rham_basis             exponent_of_different_prim

cartier_matrixdx       fct_field

charactristicdx_seriefunctions                      

cohmology_of_structure_sheaf_basisexponent_of_differentgenus              [?7h[?12l[?25h[?25l[?7lat_mostpoles

 a_number     branch_pointde_rham_basis             

 at_mostpoles cartier_matrixdx       

 at_mos_poles_formscharactristicdx_serie

 base_rin                          cohmology_of_structure_sheaf_basisexponent_of_different[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_forms



 AS.at_most_poles                      

 AS.at_most_poles_forms                [?7h[?12l[?25h[?25l[?7l(









[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1)

[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx,
 ((x^3 + x*z0^2 + y*z0)/y) * dx,
 (1/y) * dx,
 (z0/y) * dx,
 ((-x^2 + z0^2)/y) * dx,
 (x/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3 with the equation:
 z^3 - z = x*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lholomorphicdifferentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = crys[0].regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = AS.at_most_poles_forms(1)[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.cycle_type()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 - x[?7h[?12l[?25h[?25l[?7lorn in range(n0 + 1, 30):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li(m-1)/2, M - (m+3)/2 + 1):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i in range(3):

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrang[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.trace()

[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 - x[?7h[?12l[?25h[?25l[?7lorn in range(n0 + 1, 30):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....: [?7h[?12l[?25h[?25l[?7lprint(n, psp(n-n0, 3)> jprime(2*n, 2)^2)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(b))[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(omega.trace())

....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     print(omega.trace())

....: 

[?7h[?12l[?25h[?2004l0 dx
((-x)/y) dx
0 dx
0 dx
((-1)/y) dx
0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1)

  macaulay2           magma               %man                map                 %%markdown           

  macaulay2_console   magma_console       mandelbrot_plot     map_threaded        math                 

  %macro              magma_free          manifolds           maple               mathematica         >

  %magic              magmathis           manual              maple_console       mathematica_console  

 [?7h[?12l[?25h[?25l[?7lt







[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l

 matrix     

 matrix_plot

 matroids   [?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.cycle_type()[?7h[?12l[?25h[?25l[?7lroup_acion_matrices_dR(C)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lup

 group_action_matrices      group_action_matrices_log 

 group_action_matrices_dR   group_action_matrices_old 

 group_action_matrices_holo groups                    [?7h[?12l[?25h[?25l[?7l_action_matrices

 group_action_matrices     





 <unknown> [?7h[?12l[?25h[?25l[?7l_log

 group_action_matrices      group_action_matrices_log [?7h[?12l[?25h[?25l[?7l(







[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_log(AS)

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In [110], line 1
----> 1 group_action_matrices_log(AS)

File <string>:62, in group_action_matrices_log(C_AS)

File <string>:241, in at_most_poles_forms(self, pole_order, threshold)

File <string>:277, in holomorphic_combinations_forms(S, pole_order)

File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
   1525     if not err:
   1526         return (<Element>right)._mul_long(value)
-> 1527     return coercion_model.bin_op(left, right, mul)
   1528 except TypeError:
   1529     return NotImplemented

File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
   1241 if mul_method is not None:
-> 1242     res = mul_method(x)
   1243     if res is not None and res is not NotImplemented:
   1244         return res

File <string>:78, in __rmul__(self, constant)

File <string>:3, in __init__(self, C, g)

File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_log(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [111], line 1
----> 1 A, B = group_action_matrices_log(AS)

File <string>:79, in group_action_matrices_log(C_AS)

File <string>:96, in coordinates(self, basis)

File <string>:96, in <listcomp>(.0)

File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    493     """
--> 494     return self.getattr_from_category(name)
    495 
    496 cdef getattr_from_category(self, name):

File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
    505     else:
    506         cls = P._abstract_element_class
--> 507     return getattr_from_other_class(self, cls, name)
    508 
    509 def __dir__(self):

File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
    359     dummy_error_message.cls = type(self)
    360     dummy_error_message.name = name
--> 361     raise AttributeError(dummy_error_message)
    362 attribute = <object>attr
    363 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     variable_names = 'x, y'

....:     for j in range(n):

....:         variable_names += ', z' + str(j)

....:     Rxyz = PolynomialRing(F, n+2, variable_names)

....:     x, y = Rxyz.gens()[:2]

....:     z = Rxyz.gens()[2:]

....:     holo_forms = [Rxyz(omega*denom) for omega in holo_forms]

....:     A = [[] for i in range(n)]

....:     for omega in holo:

....:         for i in range(n):

....:             ei = n*[0]

....:             ei[i] = 1

....:             omega1 = omega.group_action(ei)

....:             omega1 = denom * omega1

....:             v1 = omega1.coordinates(holo_forms)

....:             A[i] += [v1]

....:     for i in range(n):

....:         A[i] = matrix(F, A[i])

....:         A[i] = A[i].transpose()

....:     return A[?7h[?12l[?25h[?25l[?7lfor j in range(n):

   variable_names += ', z' + str(j)

Rxyz = PolynomialRing(F, n+2,variable_names)

x, yRxyz.gens()[:2]

z = Rxyz.gens()[2:]

holo_forms = [Rxyz(omega*denom) for omega in holo_forms]

A = [[] for i in range(n)]

foromega in holo:

   for irange(n):

   ei =n*[0]

[i] = 1

omega1 = omega.group_action(ei)

denom * meg1

v1 = omega1.coordinates(holo_forms)

A[i]+= [v]

foriin range(n):

   A[i]= matrix(F, A[i])

A[i].transpose()

return A

[?7h[?12l[?25h[?25l[?7l....:     for j in range(n):

....:         variable_names += ', z' + str(j)

....:     Rxyz = PolynomialRing(F, n+2, variable_names)

....:     x, y = Rxyz.gens()[:2]

....:     z = Rxyz.gens()[2:]

....:     holo_forms = [Rxyz(omega*denom) for omega in holo_forms]

....:     A = [[] for i in range(n)]

....:     for omega in holo:

....:         for i in range(n):

....:             ei = n*[0]

....:             ei[i] = 1

....:             omega1 = omega.group_action(ei)

....:             omega1 = denom * omega1

....:             v1 = omega1.coordinates(holo_forms)

....:             A[i] += [v1]

....:     for i in range(n):

....:         A[i] = matrix(F, A[i])

....:         A[i] = A[i].transpose()

....:     return A

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_log(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [113], line 1
----> 1 A, B = group_action_matrices_log(AS)

Cell In [112], line 6, in group_action_matrices_log(C_AS)
      4 holo = C_AS.at_most_poles_forms(Integer(1))
      5 holo_forms = [omega for omega in holo]
----> 6 denom = LCM([denominator(omega) for omega in holo_forms])
      7 variable_names = 'x, y'
      8 for j in range(n):

Cell In [112], line 6, in <listcomp>(.0)
      4 holo = C_AS.at_most_poles_forms(Integer(1))
      5 holo_forms = [omega for omega in holo]
----> 6 denom = LCM([denominator(omega) for omega in holo_forms])
      7 variable_names = 'x, y'
      8 for j in range(n):

File /ext/sage/9.8/src/sage/misc/functional.py:251, in denominator(x)
    249 if isinstance(x, int):
    250     return 1
--> 251 return x.denominator()

AttributeError: 'as_form' object has no attribute 'denominator'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def group_action_matrices_log(AS):

....:     n = AS.height

....:     generators = []

....:     for i in range(n):

....:         ei = n*[0]

....:         ei[i] = 1

....:         generators += [ei]

....:     return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.holomorphic_differentials_basis
(

....: ))[?7h[?12l[?25h[?25l[?7l(

....: ))

....: [?7h[?12l[?25h[?25l[?7lsage: def group_action_matrices_log(AS):

....:     n = AS.height

....:     generators = []

....:     for i in range(n):

....:         ei = n*[0]

....:         ei[i] = 1

....:         generators += [ei]

....:     return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.holomorphic_differentials_basis
(

....: ))

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7lS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_log(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In [115], line 1
----> 1 A, B = group_action_matrices_log(AS)

Cell In [114], line 8, in group_action_matrices_log(AS)
      6     ei[i] = Integer(1)
      7     generators += [ei]
----> 8 return group_action_matrices(AS.at_most_poles_forms(Integer(1)), generators, basis = AS.holomorphic_differentials_basis())

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.8/src/sage/matrix/matrix0.pyx:1520, in sage.matrix.matrix0.Matrix.__setitem__()
   1518         raise IndexError("value does not have the right number of columns")
   1519     elif single_col and row_list_len != len(value_list):
-> 1520         raise IndexError("value does not have the right number of rows")
   1521 else:
   1522     if row_list_len != len(value_list):

IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def group_action_matrices_log(AS):

....:     n = AS.height

....:     generators = []

....:     for i in range(n):

....:         ei = n*[0]

....:         ei[i] = 1

....:         generators += [ei]

....:     return group_action_matrices(AS.at_most_poles_forms(1), generators, basis = AS.at_most_poles_forms(1))[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
[?2004l
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Using Python 3.11.1. Type "help()" for help.                       │
│ Enhanced for CoCalc.                                               │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_log(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [2], line 1
----> 1 AS

NameError: name 'AS' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.x*C.y], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1)

[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx,
 ((x^3 + x*z0^2 + y*z0)/y) * dx,
 (1/y) * dx,
 (z0/y) * dx,
 ((-x^2 + z0^2)/y) * dx,
 (x/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_(1)[?7h[?12l[?25h[?25l[?7lf(1)[?7h[?12l[?25h[?25l[?7lo(1)[?7h[?12l[?25h[?25l[?7lr(1)[?7h[?12l[?25h[?25l[?7lm(1)[?7h[?12l[?25h[?25l[?7ls(1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC1)[?7h[?12l[?25h[?25l[?7l,1)[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(C, 1)[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(C, 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_forms(C, 1)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [5], line 1
----> 1 at_most_poles_forms(C, Integer(1))

NameError: name 'at_most_poles_forms' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(C, 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7l(C, 1)[?7h[?12l[?25h[?25l[?7ls(C, 1)[?7h[?12l[?25h[?25l[?7lu(C, 1)[?7h[?12l[?25h[?25l[?7lp(C, 1)[?7h[?12l[?25h[?25l[?7le(C, 1)[?7h[?12l[?25h[?25l[?7lr(C, 1)[?7h[?12l[?25h[?25l[?7le(C, 1)[?7h[?12l[?25h[?25l[?7ll(C, 1)[?7h[?12l[?25h[?25l[?7ll(C, 1)[?7h[?12l[?25h[?25l[?7li(C, 1)[?7h[?12l[?25h[?25l[?7lp(C, 1)[?7h[?12l[?25h[?25l[?7lt(C, 1)[?7h[?12l[?25h[?25l[?7li(C, 1)[?7h[?12l[?25h[?25l[?7lc(C, 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: at_most_poles_superelliptic(C, 1)

[?7h[?12l[?25h[?2004l[?7h[1, x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lat_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1)

[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx,
 ((x^3 + x*z0^2 + y*z0)/y) * dx,
 (1/y) * dx,
 (z0/y) * dx,
 ((-x^2 + z0^2)/y) * dx,
 (x/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lblock_matrix([[A1, A2]])[?7h[?12l[?25h[?25l[?7lase_ring(parent(x))[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[((-x*z0 + y)/y) * dx,
 (1/y) * dx,
 (z0/y) * dx,
 ((-x^2 + z0^2)/y) * dx,
 (x/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor omega in AS.at_most_poles_forms(1):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega in AS.at_most_poles_forms(1):[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....: [?7h[?12l[?25h[?25l[?7lprint(omega.trace())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(omega, omega.trace())

....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     print(omega, omega.trace())

....: 

[?7h[?12l[?25h[?2004l((-x*z0 + y)/y) * dx 0 dx
((x^3 + x*z0^2 + y*z0)/y) * dx ((-x)/y) dx
(1/y) * dx 0 dx
(z0/y) * dx 0 dx
((-x^2 + z0^2)/y) * dx ((-1)/y) dx
(x/y) * dx 0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     print(omega, omega.trace())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(omega, omega.trace(), omega - omega.group_action([1]))

....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     print(omega, omega.trace(), omega - omega.group_action([1]))

....: 

[?7h[?12l[?25h[?2004l((-x*z0 + y)/y) * dx 0 dx (x/y) * dx
((x^3 + x*z0^2 + y*z0)/y) * dx ((-x)/y) dx ((x*z0 - x - y)/y) * dx
(1/y) * dx 0 dx (0) * dx
(z0/y) * dx 0 dx ((-1)/y) * dx
((-x^2 + z0^2)/y) * dx ((-1)/y) dx ((z0 - 1)/y) * dx
(x/y) * dx 0 dx (0) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

....: 

....:     print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l print(omega, omega.trace(), omega - omega.group_action([1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l....:         print(omega, omega.trace(), omega - omega.group_action([1]))

....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     if omega.valuation() < 0:

....:         print(omega, omega.trace(), omega - omega.group_action([1]))

....: 

[?7h[?12l[?25h[?2004l((x^3 + x*z0^2 + y*z0)/y) * dx ((-x)/y) dx ((x*z0 - x - y)/y) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.trace()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C1.x^2*C1.y.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles

 AS.at_most_poles      

 AS.at_most_poles_forms





 [?7h[?12l[?25h[?25l[?7l

 AS.at_most_poles      



 <unknown> [?7h[?12l[?25h[?25l[?7l_forms

 AS.at_most_poles      

 AS.at_most_poles_forms[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles_forms(1)[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 







 [?7h[?12l[?25h[?25l[?7lomega = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega

[?7h[?12l[?25h[?2004l[?7h((x^3 + x*z0^2 + y*z0)/y) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.valuation()

[?7h[?12l[?25h[?2004l[?7h-1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + x + 1 over Finite Field of size 3 with the equation:
 z^3 - z = x*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lpseud_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7leudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30)

[?7h[?12l[?25h[?2004l[?7h[-x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + y,
 x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + y*z0,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x*z0,
 -x^55 + x^53*z0^2 - x^54 + x^53*y - x^53*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*z0 + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 + x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*y - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^42*z0^2 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*z0 + x^40*z0^2 + x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*y*z0 + x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^33*z0^2 + x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^33 + x^32*z0 - x^31*z0^2 - x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^30*z0 - x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 - x^26*z0 + x*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x*y,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^51*y - x^51*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^45*y + x^44*y*z0 - x^44*y + x^44*z0 - x^43*y*z0 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 - x^36*z0^2 - x^36*z0 - x^35*y*z0 - x^36 + x^35*y + x^34*y*z0 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^27 + x^2,
 x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 + x^2*z0,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^47 + x^45*y*z0 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^42*y*z0 - x^42*z0 + x^41*z0^2 + x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^33*y*z0 + x^33*z0 - x^32*z0^2 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*y + x^27 + x^2*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^2*y,
 x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^44*y*z0^2 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^35*y*z0 - x^34*y*z0^2 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^26*y*z0 - x^26*y + x^26*z0 + x^2*y*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^51 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^49*z0 + x^47*y*z0^2 - x^49 + x^48*y + x^47*y*z0 + x^47*z0 - x^46*y*z0 - x^46*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*z0^2 + x^45 + x^44*z0 - x^42*y*z0^2 + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*y + x^41*z0 - x^40*z0^2 + x^41 - x^39*z0^2 - x^40 + x^38*z0^2 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^35*y*z0 + x^36 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^31*z0^2 - x^32 + x^30*z0^2 + x^29*y*z0^2 + x^31 - x^29*z0^2 + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*z0 + x^27*y*z0 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^2*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 + x^41 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 - x^32 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^3,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^45 - x^44*z0 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 - x^41 - x^39*z0^2 - x^40 + x^39*y + x^38*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^37 + x^35*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*z0^2 - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*y*z0 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^26*y + x^26*z0 + x^3*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^3*y,
 x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 - x^31*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^26*y - x^26*z0 + x^3*y*z0,
 x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^50*y*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*y - x^42*z0^2 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 + x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 - x^32 + x^31*z0 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^28 - x^27*y - x^26*z0^2 + x^27 + x^26*z0 + x^3*y*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*y + x^26*z0 + x^4,
 -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 - x^27 - x^26*z0 + x^4*z0,
 x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 - x^51 + x^49*y*z0 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 + x^49 - x^48*y - x^47*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 - x^45*y*z0^2 - x^47 + x^45*z0^2 + x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^39 - x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^36*y*z0 + x^36*z0^2 + x^37 - x^35*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^33 + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^30 + x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^26*z0 + x^4*z0^2,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^27 + x^26*z0 + x^4*y,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 - x^52 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^31*y*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 - x^27 + x^26*y + x^26*z0 + x^4*y*z0,
 x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 - x^52*z0^2 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 - x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^39 - x^38*y + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y + x^33*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^30 + x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^27*y*z0 - x^26*y*z0^2 + x^28 - x^26*z0^2 + x^26*y - x^26*z0 + x^4*y*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0 + x^39*z0^2 - x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y - x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^26*y*z0 - x^26*y + x^5*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*z0^2 + x^51*z0 - x^50*y*z0 - x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 - x^48*y + x^47*y*z0 + x^46*y*z0^2 - x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^44 - x^43*y - x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*z0^2 - x^38 + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 - x^35 + x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 - x^33 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y + x^26*z0^2 - x^27 + x^5*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^5*y,
 -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*z0^2 + x^42 + x^40*z0 - x^39*z0^2 + x^40 + x^39*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^31*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^26*y*z0 + x^27 - x^26*z0 + x^5*y*z0,
 -x^55 + x^53*z0^2 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^50*y*z0^2 - x^52 + x^50*y*z0 - x^50*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^45 + x^43*z0^2 - x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*z0 - x^37*z0^2 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^35*z0 + x^34*y - x^34*z0 - x^33*y*z0 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y - x^31*z0^2 + x^32 + x^31*z0 + x^29*y*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^26*z0 + x^5*y*z0^2,
 x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^6,
 x^55 + x^54*z0 - x^54 - x^53*y - x^52*y*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^49*y*z0^2 + x^51 - x^50*y + x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48*z0 - x^47*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^47 - x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*z0 + x^40*y*z0^2 - x^42 - x^41*y + x^39*y*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*z0^2 - x^39 + x^38*y - x^38*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0 + x^33 + x^32*y - x^30*y*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^29 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^6*y,
 -x^54*z0 - x^53*z0^2 - x^54 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27 - x^26*z0 + x^6*y*z0,
 -x^55 - x^54*z0 + x^53*y + x^52*y*z0 + x^52*z0^2 - x^50*y*z0^2 - x^52 - x^51*z0 + x^50*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^48 - x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y + x^46*z0 + x^45*z0^2 - x^45*z0 - x^44*y*z0 + x^45 + x^44*z0 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^41*z0^2 - x^41*y - x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^37*y + x^37*z0 + x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y + x^34*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^32*y + x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^28*z0^2 + x^29 - x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y - x^26*z0 + x^6*y*z0^2,
 x^54*z0 + x^53*z0^2 + x^54 - x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 + x^50 + x^48*y*z0 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^48 + x^47*y + x^47*z0 + x^47 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 - x^42*z0^2 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 + x^40*y*z0^2 + x^42 - x^41*z0 - x^40*z0^2 - x^41 + x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^33*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 - x^31*y*z0^2 - x^33 + x^32*z0 + x^31*z0^2 + x^32 - x^30*z0^2 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^26*z0^2 + x^27 - x^26*z0 + x^7*z0^2,
 x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^46*y - x^46*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^26*y + x^7*y,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 + x^51*y + x^51*z0 - x^49*y*z0^2 - x^50*y - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 - x^49 + x^48*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^46*y*z0 + x^46*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 - x^46 + x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 + x^42*y*z0^2 + x^42*y*z0 - x^42*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 - x^42 + x^41*y - x^41*z0 + x^40*z0^2 - x^40*z0 - x^39*z0^2 - x^40 + x^39*y - x^38*y*z0 + x^38*y - x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^37*y - x^37 - x^36*y + x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y + x^35*z0 - x^33*y*z0^2 + x^35 - x^33*y*z0 - x^34 + x^33*y - x^32*y*z0 + x^31*y*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*z0^2 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^29*y*z0 - x^29*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^28 - x^27*y + x^26*y - x^26*z0 + x^7*y*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^8,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^26*z0 + x^8*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^50 + x^48*z0^2 - x^49 + x^48*y - x^48*z0 + x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^41*y*z0^2 + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 + x^38 + x^36*y*z0 + x^36*z0^2 - x^37 - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 + x^32*y*z0^2 - x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^32*z0 - x^30*y*z0^2 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^8*z0^2,
 x^54*z0 + x^53*z0^2 - x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*z0^2 + x^47*y*z0^2 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y + x^38*z0^2 - x^37*y*z0^2 + x^37*y*z0 + x^37*z0^2 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^29 + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y - x^26*y + x^8*y*z0,
 x^55 - x^53*z0^2 - x^53*y + x^53*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^50 + x^49*y + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 - x^43*y + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^34*y - x^33*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0 - x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0^2 + x^26*z0 + x^8*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^40*y*z0 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 - x^37*z0^2 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^31*y*z0 - x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^26*z0 + x^9*z0,
 -x^54 + x^52*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 - x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^45*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^43*z0^2 - x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^42*y - x^42*z0 - x^40*y*z0^2 - x^42 + x^41*y + x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^38 + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^35*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^31*y*z0^2 + x^33 - x^32*y + x^30*y*z0^2 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 + x^26*y + x^26*z0 + x^9*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*z0^2 + x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^37*z0^2 + x^38 - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y + x^36*z0 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 - x^28*z0^2 + x^29 - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^9*y*z0,
 x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 + x^53 + x^52*y + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y - x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 + x^49*y - x^48*y*z0 - x^47*y*z0^2 + x^47*y*z0 + x^46*y*z0^2 + x^48 - x^46*z0^2 + x^47 - x^45*y*z0 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^37*y + x^37*z0 + x^35*y*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 - x^26*y + x^26*z0 + x^9*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^27*z0 + x^26*y*z0 + x^10,
 x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*y + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*y + x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*z0 + x^32*z0^2 - x^32*z0 + x^31*y*z0 + x^32 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 + x^26*y*z0 - x^26*z0 + x^10*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 - x^46 - x^44*y*z0 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 + x^41 - x^40 - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 + x^38*z0 + x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 - x^36*y*z0 - x^37 - x^36*y + x^36*z0 + x^35*z0^2 + x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^33*y*z0 - x^33*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y + x^32*z0 - x^32 + x^31 + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 - x^29*z0 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 + x^28 + x^27*y - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^10*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^52*y*z0 + x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*y + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^42 + x^41*y - x^41 - x^39*z0^2 + x^39*z0 - x^38*z0^2 + x^39 + x^38*y - x^38*z0 + x^38 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y + x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 + x^33 - x^32*y + x^31*z0^2 + x^32 - x^30*z0^2 - x^30*z0 + x^29*z0^2 - x^30 - x^29*y + x^29*z0 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^10*y*z0^2,
 x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27 - x^26*y - x^26*z0 + x^11,
 x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^26*y*z0 - x^26*y + x^11*z0,
 x^55 - x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 - x^49*y*z0 - x^49*z0^2 + x^50 - x^49*y + x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^47 - x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^44 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 + x^36*y + x^35*z0^2 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^34 - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^11*z0^2,
 -x^54*z0 - x^53*z0^2 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*y + x^11*y,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^26*z0 + x^11*y*z0,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^47*y*z0^2 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^43*y*z0^2 + x^44*y + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*z0^2 - x^38 - x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^35*z0^2 - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^33*y*z0^2 + x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y - x^33*z0 - x^33 + x^32*y - x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*z0^2 + x^29 - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*z0 - x^26*y*z0 - x^26*z0^2 - x^27 - x^26*y - x^26*z0 + x^11*y*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27 - x^26*y + x^26*z0 + x^12,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 - x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*z0^2 - x^38 - x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 - x^27 - x^26*y - x^26*z0 + x^12*z0,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 + x^52 + x^51*y + x^51*z0 + x^50*z0^2 + x^51 + x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 + x^46 - x^44*y*z0 - x^44*z0^2 - x^45 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^39*y*z0^2 + x^41 - x^39*z0^2 + x^39*y - x^39*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^30*y*z0^2 - x^32 + x^30*z0^2 - x^30*y + x^30*z0 - x^29*z0^2 - x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^28*y - x^28*z0 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^12*z0^2,
 -x^55 + x^53*z0^2 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27 + x^26*z0 + x^12*y,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 + x^46*y*z0^2 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*y - x^41 + x^40*z0 - x^39*z0^2 - x^40 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*y - x^34*z0 + x^32*y*z0^2 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 - x^31*z0 + x^30*z0^2 + x^31 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^26*y*z0 + x^27 + x^26*y + x^12*y*z0,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 + x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 - x^50 + x^49 - x^48*y + x^48*z0 - x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*z0 - x^45*y*z0 + x^45*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^43*y*z0 + x^43*z0^2 - x^44 - x^43*z0 - x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 - x^38 - x^36*y*z0 + x^36*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^34*z0 + x^33*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 - x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 + x^28*z0 + x^27*y*z0 - x^27*z0^2 - x^28 + x^27*z0 - x^26*y*z0 + x^27 - x^26*y + x^12*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*y + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^13,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^48*y - x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^45*y*z0^2 - x^46*y + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 + x^36*z0^2 - x^36*y + x^35*y*z0 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^34 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^29*y*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^52 - x^51*y + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^26*z0 + x^13*y,
 -x^54*z0 - x^53*z0^2 + x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*y - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^44*z0^2 - x^43*y*z0^2 - x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^43*y - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^41 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 + x^32*y - x^32*z0 + x^32 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y + x^28*z0^2 - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y - x^26*y + x^26*z0 + x^13*y*z0,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^52*z0^2 + x^51*y*z0^2 + x^52*y - x^52*z0 + x^51*y*z0 - x^50*y*z0^2 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^51 - x^50*y + x^49*y*z0 + x^49*z0^2 - x^49*y - x^49*z0 + x^48*y*z0 - x^47*y*z0^2 + x^48*y + x^47*z0^2 - x^46*y*z0^2 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^45*z0^2 + x^46 - x^45*y - x^45*z0 + x^44*y*z0 + x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*z0 - x^40*z0^2 + x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^36*y*z0^2 + x^38 - x^36*y*z0 - x^36*z0^2 + x^35*y*z0^2 - x^36*y + x^35*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^35 - x^34*y + x^34*z0 + x^33*y*z0 + x^33*z0^2 - x^32*y*z0^2 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^27*y*z0^2 - x^28*z0 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^13*y*z0^2,
 x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^46*y - x^46*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 + x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 + x^36*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 + x^27 + x^14,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^51*y + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^49 + x^47*z0^2 - x^46*y*z0^2 + x^48 - x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 - x^39*y*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 + x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 + x^37 - x^36*y + x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 - x^30*y*z0^2 - x^32 - x^31*z0 - x^30*z0^2 - x^29*y*z0^2 - x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0 + x^14*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^51*y*z0 - x^51*z0^2 - x^51*y - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^47*y*z0 - x^46*y*z0^2 + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y - x^43*z0 + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 - x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 - x^26*y + x^26*z0 + x^14*y,
 -x^55 + x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^51*y*z0^2 - x^53 - x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^51*y + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*z0 + x^46*y*z0^2 + x^48 - x^47*z0 - x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^37*z0^2 - x^37*y + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^33*y*z0 + x^32*y*z0^2 + x^34 + x^33*y - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^28*z0^2 + x^29 + x^28*y + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^26*y*z0 - x^26*z0 + x^14*y*z0,
 x^55 + x^54*z0 - x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 + x^52 - x^50*y*z0 - x^49*y*z0^2 + x^50*y - x^49*y*z0 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^43*y*z0 + x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 + x^41*y - x^41*z0 + x^40*z0^2 + x^41 - x^40*z0 - x^38*y*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 - x^34*y - x^34*z0 - x^33*z0^2 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 - x^32 + x^31*z0 - x^30*z0^2 + x^29*y*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 - x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^26*y + x^14*y*z0^2,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^41 - x^40*y - x^40*z0 - x^39*z0^2 - x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 - x^31*y + x^31*z0 + x^30*z0^2 + x^31 + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^15,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^47*z0 - x^45*y*z0^2 + x^47 - x^46*z0 - x^45*y*z0 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^45 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*z0 - x^42*z0^2 - x^41*y*z0^2 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 + x^41*y + x^41*z0 + x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 + x^39*z0 + x^38*y*z0 + x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 - x^38 - x^36*y*z0 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 - x^35*y*z0 - x^36 - x^35*z0 + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*z0 + x^33*z0^2 + x^32*y*z0^2 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^31*y*z0^2 - x^32*y - x^32*z0 - x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*z0 - x^29*y*z0 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^26*z0^2 + x^27 + x^26*y + x^15*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^52*y*z0 - x^51*y*z0^2 - x^53 + x^52*z0 + x^51*z0^2 + x^52 + x^51*y - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 + x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^44*y*z0^2 + x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*y - x^43*z0 - x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*z0 - x^40*z0 - x^39*y*z0 - x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^34*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^32*z0 + x^30*y*z0 + x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y + x^28*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 - x^27 - x^26*z0 + x^15*y*z0,
 -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 - x^52*y - x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*y + x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^45*y*z0^2 + x^46*y + x^45*y*z0 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 + x^42 + x^41*z0 + x^40*z0^2 - x^39*y*z0^2 - x^41 - x^40*z0 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*y*z0 + x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^32*y*z0 + x^32*z0^2 - x^33 - x^32*z0 + x^31*z0^2 + x^30*y*z0^2 + x^32 + x^31*z0 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 - x^26*z0 + x^15*y*z0^2,
 x^55 - x^53*z0^2 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^43*y + x^41*y*z0^2 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^41*z0 + x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^32*y*z0^2 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^28*y*z0 + x^28*z0^2 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27 + x^26*y - x^26*z0 + x^16,
 x^55 - x^53*z0^2 + x^54 - x^53*y + x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 - x^50*y*z0^2 - x^52 - x^50*y*z0 + x^50*z0^2 - x^51 - x^50*z0 - x^49*y + x^48*y*z0 + x^48*z0^2 + x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 - x^48 - x^47*z0 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 - x^46 + x^45*y + x^45*z0 - x^44*z0^2 + x^45 - x^44*y - x^43*z0^2 + x^43*y - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^40*y*z0^2 + x^42 - x^41*y - x^40*z0^2 + x^41 + x^40*z0 - x^39*z0^2 - x^38*y*z0^2 + x^38*y*z0 - x^39 - x^38*y + x^38*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 + x^37*y - x^37*z0 + x^36*y*z0 + x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^35*z0^2 + x^36 + x^35*y - x^35*z0 + x^34*z0^2 - x^35 - x^34*y + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^31*y*z0^2 - x^33 + x^32*y + x^31*z0^2 - x^32 - x^31*z0 + x^30*z0^2 - x^29*y*z0 + x^28*y*z0^2 + x^30 + x^29*y - x^29*z0 + x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*y - x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^26*y - x^26*z0 + x^16*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 + x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^40*y*z0 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*y - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*y - x^37*y*z0 - x^37*z0^2 - x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 + x^34*y - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*z0 + x^31*y*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*y + x^29*z0^2 - x^28*y*z0^2 - x^30 - x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*y + x^27*z0 + x^26*y*z0 + x^27 + x^16*y*z0,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^52*z0^2 - x^51*y*z0^2 - x^52*y + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^50*y*z0^2 + x^51*z0 - x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*y - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 + x^49 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 + x^43*y*z0^2 - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 - x^41*y*z0 - x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 + x^40*z0^2 - x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y - x^38*z0 - x^37*y*z0 - x^37*y + x^36*y*z0 + x^36*z0^2 + x^37 - x^34*y*z0^2 - x^36 - x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 - x^31*z0^2 + x^32 - x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 - x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 + x^28 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^26*y - x^26*z0 + x^16*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 + x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^51*z0^2 - x^51*y + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^48 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*y - x^41*y*z0 + x^41*z0^2 - x^42 - x^41*y + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 + x^32*y*z0 - x^32*z0^2 + x^33 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y - x^26*z0 + x^17,
 x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 + x^53 + x^52 - x^51*y - x^51 + x^50*y + x^48*y*z0^2 + x^47*y*z0^2 + x^49 - x^48*y + x^47 + x^46 - x^45 + x^42*y*z0^2 + x^42*y + x^41*y - x^39*y*z0^2 - x^41 + x^38*y*z0^2 + x^40 + x^36*y*z0^2 - x^38 + x^35*y*z0^2 + x^37 + x^36*y - x^36 + x^35 - x^33*y - x^32*y + x^32 - x^31 + x^29 - x^28 - x^27*y + x^26*z0^2 + x^27 + x^26*y + x^17*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 + x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 + x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^41*y*z0^2 - x^43 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 + x^41 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 + x^34 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y - x^27 - x^26*y + x^26*z0 + x^17*y,
 x^54*z0 + x^53*z0^2 - x^54 - x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 - x^49*z0^2 + x^50 + x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^43*y*z0 + x^43*z0^2 - x^44 + x^43*z0 - x^42*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^42 + x^41*y - x^41*z0 - x^40*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 + x^37*y + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^35 - x^34*z0 - x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^33 - x^32*y + x^32*z0 + x^31*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*z0 + x^29*y*z0 - x^28*y*z0^2 - x^29*y - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 + x^27*y - x^27*z0 + x^26*y*z0 - x^27 + x^26*y + x^17*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 - x^40*y*z0 - x^41 - x^40*z0 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y + x^37*z0^2 + x^37*y - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^35 + x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^29*y + x^28*y*z0 - x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*z0 + x^18*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^54 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 - x^52*y + x^52*z0 + x^51*y*z0 + x^50*y*z0^2 - x^50*y*z0 - x^50*z0^2 - x^51 + x^50*y - x^49*y*z0 - x^48*y*z0^2 + x^49*y + x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 - x^47*z0 - x^46*z0^2 + x^46*y + x^46*z0 + x^45*y*z0 - x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^43*y*z0^2 - x^44*y + x^43*y*z0 - x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 - x^42*z0^2 + x^41*y*z0^2 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*z0 + x^39*y*z0^2 - x^41 - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y + x^37*y*z0 - x^37*z0^2 - x^38 + x^36*y*z0 + x^36*z0^2 + x^36*y - x^36*z0 + x^35*y*z0 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 - x^34*y*z0 + x^33*y*z0^2 - x^35 + x^34*y - x^34*z0 + x^33*z0^2 - x^32*y*z0^2 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 - x^28*z0 - x^27*y*z0 + x^27*z0^2 - x^28 + x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 - x^27 + x^18*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^41 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y - x^36*z0 + x^34*y*z0^2 + x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^18*y,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^52*y*z0 + x^51*y*z0^2 - x^52*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^46*y - x^46*z0 + x^44*y*z0^2 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 - x^41*y + x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 + x^38*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y - x^32*z0 + x^32 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^18*y*z0,
 x^54 - x^53*z0 - x^52*z0^2 + x^53 - x^52*y + x^51*y*z0 + x^50*y*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^48 - x^47*y - x^46*y*z0 - x^47 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^46 + x^44*y*z0 - x^45 + x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*y + x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*z0 + x^38*z0^2 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^36 + x^34*y*z0 - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^33 + x^32*y + x^32*z0 - x^32 + x^31 - x^30*z0 + x^29*y + x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 - x^26*y + x^18*y*z0^2,
 -x^55 + x^53*z0^2 - x^54 + x^53*y + x^53*z0 - x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*y + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^46*z0 - x^45*y*z0 - x^44*y*z0^2 - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^43*y - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^42 + x^41*z0 + x^41 + x^40*y - x^40*z0 - x^39*z0^2 + x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 - x^38 + x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^34*y + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^33 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^28*y*z0 - x^28*z0^2 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^27*y + x^26*y + x^26*z0 + x^19,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 + x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 + x^51 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*z0^2 - x^45*y*z0^2 - x^47 + x^46*z0 + x^45*y*z0 + x^45*z0^2 + x^46 + x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 + x^40*y*z0^2 - x^42 - x^41*y - x^41*z0 - x^40*z0 - x^39*z0^2 - x^39*y - x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^39 + x^38*y + x^37*y*z0 + x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*y + x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*z0^2 + x^34 - x^33*z0 - x^32*y*z0 + x^33 + x^32*y + x^32*z0 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^30*y + x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^28*y*z0 + x^29 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^19*z0^2,
 x^54*z0 + x^53*z0^2 - x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 + x^52*y + x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^52 - x^51*z0 - x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 + x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 - x^46*y - x^46*z0 - x^44*y*z0^2 - x^45*y - x^45*z0 - x^44*z0^2 + x^43*y*z0^2 + x^45 + x^44*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 + x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^41*y + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^40 - x^39*y - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*y - x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^36*z0 - x^34*y*z0^2 + x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*y - x^32*z0 - x^32 + x^31*z0 + x^30*z0^2 - x^31 + x^30*y + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^29*y + x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^19*y,
 x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^51*y*z0 - x^51*z0^2 - x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 - x^47*y*z0 - x^46*y*z0^2 - x^48 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 + x^40*z0 + x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 + x^26*y*z0 + x^19*y*z0,
 x^55 - x^53*z0^2 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 + x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^49*z0 - x^48*y*z0 + x^48*z0^2 + x^48*y - x^48 - x^47*y - x^47*z0 + x^46*y*z0 - x^45*y*z0^2 + x^47 - x^46*y - x^46 - x^45*y + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^42*y*z0^2 + x^44 - x^43*y + x^43*z0 + x^42*y*z0 + x^42*z0^2 + x^43 - x^42*y + x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^41*y + x^41*z0 + x^40*z0^2 + x^41 + x^40*z0 + x^39*z0^2 + x^40 - x^39*z0 + x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 + x^37*y + x^36*y*z0 + x^36*y - x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*y*z0 - x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 - x^33*y*z0 - x^33*z0^2 - x^34 + x^33*y - x^33*z0 + x^32*y*z0 + x^32*y - x^32*z0 - x^32 - x^31*z0 - x^31 + x^30*z0 - x^29*y*z0 + x^28*y*z0^2 - x^30 + x^29*z0 + x^28*y*z0 - x^29 - x^28*y + x^28*z0 - x^27*y*z0 - x^27*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*y - x^26*z0 + x^19*y*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^41*y*z0^2 + x^43 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32*z0 + x^32 + x^31*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^26*y*z0 - x^27 + x^26*y + x^20*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y + x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 - x^51*y*z0 - x^51*z0^2 - x^52 - x^51*y - x^51*z0 + x^49*y*z0^2 + x^51 - x^50*y - x^49*z0^2 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 - x^46 + x^45*y + x^45*z0 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 + x^43*z0^2 + x^44 - x^42*y*z0 - x^41*y*z0^2 + x^42*y - x^41*y*z0 - x^41*z0^2 + x^41*y + x^41*z0 + x^40*z0 + x^39*z0^2 + x^38*y*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 - x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^36*z0^2 + x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^35*y*z0 - x^35*z0^2 + x^34*y*z0^2 + x^36 + x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 - x^32*y*z0^2 - x^33*y + x^32*y*z0 + x^32*z0^2 - x^32*y - x^32*z0 + x^30*y*z0^2 - x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 + x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^28*z0 - x^27*z0^2 - x^26*y*z0^2 + x^28 + x^26*z0^2 - x^27 + x^26*y + x^26*z0 + x^20*z0^2,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 - x^53 - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y + x^48*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^46*z0^2 - x^45*y*z0^2 + x^46*y - x^46*z0 - x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^41 + x^39*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*y - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^33*y*z0 - x^32*y*z0^2 + x^34 - x^32*y*z0 + x^32*z0^2 + x^32*z0 - x^32 + x^31*z0 - x^30*z0^2 + x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^29 + x^28*y + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^26*z0 + x^20*y*z0,
 -x^55 + x^53*z0^2 + x^53*y - x^53*z0 - x^52*z0^2 - x^51*y*z0^2 + x^53 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^51*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*y*z0 + x^48*y*z0^2 + x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 + x^45*y + x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 + x^42*y + x^41*y*z0 - x^41*z0^2 + x^41*y - x^41*z0 - x^40*z0^2 - x^39*z0^2 - x^40 + x^39*y + x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*z0 + x^37*y*z0 + x^38 - x^37*z0 - x^36*z0^2 - x^37 + x^36*y - x^36*z0 - x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^34*y*z0 - x^34*z0^2 + x^33*y*z0^2 - x^34*z0 - x^33*y*z0 + x^32*y*z0^2 - x^33*y - x^32*y*z0 - x^32*z0^2 - x^32*y + x^32*z0 - x^31*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*z0 - x^28*y*z0 + x^28*z0 + x^28 - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^27 + x^26*y + x^20*y*z0^2,
 x^55 - x^53*z0^2 + x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 - x^53 - x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*z0 + x^44*y*z0^2 - x^46 - x^45*y + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*y*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*z0^2 - x^38 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^32*y*z0^2 - x^34 - x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^33 - x^32*y + x^32*z0 + x^31*y*z0 - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y - x^26*z0 + x^21*z0,
 -x^55 + x^54*z0 - x^53*z0^2 - x^54 + x^53*y - x^53*z0 - x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^52 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 + x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y + x^48*z0 - x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 - x^47 - x^46*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 + x^45*y - x^44*y*z0 + x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y + x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^39*y*z0^2 + x^39*z0^2 - x^39*y - x^39*z0 - x^38*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*y - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 + x^33 + x^32*y + x^32*z0 - x^30*z0^2 + x^30*y + x^30*z0 + x^29*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0^2 + x^29 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^26*y - x^26*z0 + x^21*z0^2,
 x^54*z0 + x^53*z0^2 + x^54 + x^53*z0 - x^52*y*z0 - x^51*y*z0^2 - x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 + x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 + x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 - x^45*z0^2 + x^44*y*z0^2 + x^46 - x^43*y*z0^2 - x^45 + x^44*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*y + x^43*z0 + x^42*z0^2 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 - x^41*y + x^41*z0 - x^39*z0^2 - x^40 - x^39*y + x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^37*y*z0 - x^36*y*z0^2 + x^37*y + x^37*z0 - x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*y - x^35*y*z0 + x^35*z0^2 + x^34*y*z0^2 - x^36 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 - x^32*y*z0^2 - x^34 - x^33*y + x^33*z0 + x^32*y*z0 - x^33 + x^32*y - x^32*z0 - x^31*z0^2 - x^30*z0^2 + x^31 + x^30*y - x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^28*y*z0 + x^27*y*z0^2 - x^29 - x^28*y - x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 - x^27 - x^26*y - x^26*z0 + x^21*y*z0^2,
 -x^55 + x^53*z0^2 + x^54 + x^53*y - x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*z0^2 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 - x^50 - x^49*z0 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*z0 - x^47*y*z0 + x^46*y*z0^2 + x^48 - x^47*y - x^47*z0 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*z0 - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^43 + x^42*z0 + x^41*z0^2 + x^42 + x^41*y + x^40*y*z0 - x^41 + x^40*z0 - x^39*z0^2 + x^40 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 - x^37*y + x^37*z0 + x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y + x^32 - x^31*z0 + x^30*z0^2 - x^31 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^28*y - x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 - x^26*y*z0 + x^26*y - x^26*z0 + x^22*z0,
 -x^55 + x^53*z0^2 + x^53*y + x^53*z0 + x^52*z0^2 - x^51*y*z0^2 - x^52*z0 - x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 - x^49*y*z0 + x^48*y*z0^2 - x^50 + x^49*z0 + x^48*z0^2 + x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 - x^47*y*z0 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*z0 - x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*y - x^44*z0 + x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^40*y*z0^2 + x^41*z0 - x^41 - x^40*z0 - x^39*z0^2 - x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^37*y*z0 + x^38 - x^37*z0 - x^36*y*z0 + x^36*z0^2 + x^35*y*z0^2 - x^37 - x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^36 - x^35*y + x^35*z0 - x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 + x^35 - x^32*y*z0^2 + x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^32*z0 + x^32 + x^31*z0 + x^30*z0^2 + x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^28*y*z0 + x^29 + x^27*y*z0 + x^27*z0^2 - x^26*y*z0^2 + x^28 - x^27*y - x^27 + x^26*z0 + x^22*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 + x^41*y - x^41*z0 + x^40*z0 + x^39*z0^2 - x^40 + x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 + x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^34 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 - x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 - x^31 - x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 + x^26*y + x^22*y,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^52 + x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 + x^48*y - x^48*z0 - x^46*y*z0^2 - x^48 + x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^44*y*z0^2 + x^46 + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 + x^41*y - x^41*z0 - x^41 + x^39*z0^2 + x^40 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^38*z0 - x^37*z0^2 + x^38 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 + x^34*y*z0^2 - x^36 + x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 - x^32*y + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^29*z0 + x^28*z0^2 - x^29 - x^28*y + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*y + x^26*z0 + x^22*y*z0,
 x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*y + x^51*z0^2 + x^50*y*z0^2 + x^52 + x^51*y + x^51*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^50 + x^49*z0 - x^48*z0^2 + x^47*y*z0^2 - x^49 - x^48*y + x^48*z0 - x^47*y*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 + x^47*y + x^46*y*z0 - x^46*z0^2 - x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 - x^45*z0^2 - x^46 - x^45*y + x^45*z0 + x^44*y*z0 - x^44*z0^2 - x^45 + x^44*y - x^44*z0 - x^43*y*z0 - x^43*z0^2 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 - x^42*y + x^41*z0^2 + x^42 + x^40*z0^2 - x^41 + x^40*z0 - x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 - x^38*y - x^36*y*z0^2 - x^38 - x^37*y - x^37*z0 + x^36*z0^2 - x^35*y*z0^2 - x^37 - x^36*y + x^36*z0 + x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^34*z0 + x^32*y*z0^2 + x^34 + x^33*y + x^32*z0^2 - x^33 + x^32 - x^31*z0 + x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 + x^29*y + x^27*y*z0^2 + x^28*y - x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^27 + x^26*z0 + x^22*y*z0^2,
 x^55 - x^54*z0 + x^53*z0^2 - x^53*y + x^53*z0 + x^52*y*z0 - x^51*y*z0^2 - x^51*y*z0 + x^51*z0^2 + x^52 + x^50*z0^2 - x^49*y*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 + x^49*z0^2 + x^48*y*z0^2 + x^50 + x^48*y*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 - x^48*y - x^47*y*z0 + x^46*y*z0^2 + x^47*y - x^46*z0^2 + x^45*y*z0^2 - x^47 + x^45*y*z0 - x^44*y*z0^2 + x^46 + x^45*y - x^45*z0 + x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 + x^43*z0 - x^42*y*z0 - x^41*y*z0^2 - x^42*y - x^41*y*z0 + x^41*z0^2 + x^41*z0 - x^40*z0 - x^39*z0^2 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^35*y*z0 - x^34*y*z0^2 - x^36 - x^35*y + x^35*z0 + x^34*y*z0 + x^34*z0^2 + x^33*y*z0^2 - x^34*z0 + x^33*y*z0 + x^32*y*z0^2 - x^33*y + x^32*y*z0 - x^32*z0^2 + x^32*y - x^32*z0 + x^31*z0 + x^30*z0^2 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y - x^26*z0 + x^23,
 x^55 - x^53*z0^2 - x^53*y + x^51*y*z0^2 - x^53 - x^51*z0^2 + x^52 + x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*z0 - x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 + x^49 - x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 - x^45*y - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 + x^43*z0 + x^42*y*z0 + x^41*y*z0^2 - x^42*y - x^41*y*z0 - x^41*z0^2 - x^41*y - x^41*z0 - x^39*y*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*z0 + x^37*y*z0 - x^37*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 - x^36*y - x^36*z0 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*z0 - x^32*y*z0^2 + x^33*y - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 + x^30*y*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^28*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^23*z0,
 -x^55 - x^54*z0 + x^53*y + x^52*y*z0 - x^52*z0 - x^51*z0^2 - x^52 - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 - x^50*y - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^49*y - x^49*z0 - x^48*y*z0 - x^48*z0^2 + x^47*y*z0^2 + x^49 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^48 + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 - x^46*y + x^45*y*z0 - x^44*y*z0^2 + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 + x^44*z0 + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 - x^44 - x^43*y + x^42*y*z0 - x^41*y*z0^2 + x^43 - x^42*y - x^42*z0 - x^41*z0^2 - x^41*y - x^39*y*z0^2 - x^41 + x^40*z0 + x^39*z0^2 - x^38*y*z0^2 - x^40 + x^39*y - x^39*z0 + x^38*y*z0 + x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*z0 - x^37*z0^2 + x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 - x^35*z0 - x^34*y*z0 - x^34*z0^2 + x^34*y - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y + x^33*z0 + x^32*z0^2 + x^32*y + x^30*y*z0^2 + x^32 - x^31*z0 - x^30*z0^2 + x^29*y*z0^2 + x^31 - x^30*y + x^30*z0 - x^29*y*z0 - x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*z0 + x^28*z0^2 + x^29 - x^28*y - x^28*z0 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27 - x^26*y + x^23*z0^2,
 x^55 - x^53*z0^2 - x^54 - x^53*y + x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^51*y + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*z0 - x^46*y*z0^2 - x^48 + x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 - x^46 - x^45*y - x^45*z0 + x^44*z0^2 - x^43*y*z0^2 + x^44*y + x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 - x^42*y*z0 + x^41*y*z0^2 + x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41 - x^40*z0 + x^39*z0^2 - x^40 - x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y - x^37*z0^2 + x^37*y - x^36*z0^2 - x^35*y*z0^2 - x^37 + x^36*y + x^35*y*z0 + x^34*y*z0^2 + x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 + x^34*z0 + x^33*y*z0 - x^32*y*z0^2 - x^34 - x^33*y - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*z0 + x^32 + x^31*z0 - x^30*z0^2 + x^31 + x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y + x^28*z0^2 - x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y - x^26*y*z0 + x^26*z0 + x^23*y*z0,
 -x^55 + x^54*z0 - x^53*z0^2 + x^53*y - x^53*z0 - x^52*y*z0 - x^52*z0^2 + x^51*y*z0^2 + x^53 + x^52*z0 + x^51*y*z0 + x^51*z0^2 + x^50*y*z0^2 - x^52 - x^51*y - x^50*y*z0 - x^50*z0^2 - x^49*y*z0^2 - x^51 - x^50*y - x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^49*y - x^48*z0^2 + x^47*y*z0^2 - x^48*y - x^48*z0 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*z0 + x^46*z0^2 - x^45*y*z0^2 + x^47 + x^46*y + x^46*z0 + x^45*y*z0 - x^45*z0^2 - x^44*y*z0^2 + x^46 - x^45*z0 - x^44*y*z0 + x^43*y*z0^2 + x^45 + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y + x^43*z0 - x^42*z0^2 - x^43 - x^42*y + x^42*z0 + x^41*y*z0 + x^41*z0^2 - x^41*y - x^41*z0 - x^40*z0^2 - x^40*z0 + x^38*y*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 - x^39 + x^37*y*z0 + x^37*z0^2 - x^38 - x^37*y + x^36*y*z0 + x^36*z0^2 - x^35*y*z0^2 - x^36*z0 + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 - x^36 + x^35*z0 - x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 + x^35 - x^34*y - x^34*z0 + x^34 + x^33*y - x^33*z0 - x^32*y*z0 + x^32*y + x^32*z0 + x^31*z0^2 + x^31*z0 - x^29*y*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 + x^30 - x^28*y*z0 - x^28*z0^2 + x^28*y - x^28*z0 - x^27*y*z0 + x^27*z0^2 + x^26*y*z0^2 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y + x^23*y*z0^2,
 -x^54*z0 - x^53*z0^2 + x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 - x^52*y + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*z0^2 + x^49*y*z0^2 - x^50*y + x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^50 - x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 + x^44*y*z0^2 + x^46 - x^45*y + x^45*z0 - x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 - x^45 + x^44*y + x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^44 + x^43*y - x^43*z0 - x^42*y*z0 + x^41*y*z0^2 + x^43 - x^42*y + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*z0 - x^40*y*z0 + x^41 + x^40*z0 - x^39*y*z0 + x^39*z0^2 - x^40 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 - x^39 - x^38*y - x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^37*y + x^37*z0 - x^36*z0^2 - x^35*y*z0^2 - x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^35 - x^34*y + x^34*z0 - x^33*y*z0 - x^32*y*z0^2 - x^34 + x^33*y - x^32*y*z0 + x^32*z0^2 - x^33 + x^32*z0 + x^31*y*z0 - x^32 - x^31*z0 + x^30*y*z0 - x^30*z0^2 + x^31 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 + x^30 + x^29*y + x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^29 - x^28*y - x^27*z0^2 + x^26*y*z0^2 - x^28 + x^27*y + x^27*z0 - x^26*y*z0 - x^27 + x^26*z0 + x^24*z0,
 x^54*z0 + x^53*z0^2 + x^53*z0 - x^52*y*z0 + x^52*z0^2 - x^51*y*z0^2 - x^53 - x^52*z0 - x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^50*z0 + x^48*y*z0^2 + x^50 - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^47*y + x^47*z0 - x^46*y*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^45*y*z0 + x^44*y*z0^2 + x^45*y - x^43*y*z0^2 - x^44*y + x^44*z0 - x^42*y*z0^2 + x^44 + x^43*z0 + x^42*z0^2 - x^41*y*z0^2 - x^42*y - x^42*z0 - x^41*y*z0 + x^41*z0^2 - x^40*y*z0^2 - x^41*y + x^41*z0 - x^39*y*z0^2 - x^41 + x^39*y - x^38*z0^2 - x^37*y*z0^2 - x^37*y*z0 + x^37*z0^2 + x^36*y*z0^2 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^36*y - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^33*y*z0^2 + x^35 - x^34*z0 - x^33*z0^2 + x^32*y*z0^2 + x^33*y + x^33*z0 + x^32*y*z0 - x^32*z0^2 + x^31*y*z0^2 + x^32*y - x^32*z0 + x^30*y*z0^2 + x^32 - x^30*y + x^29*z0^2 + x^28*y*z0^2 + x^28*y*z0 - x^28*z0^2 - x^27*y*z0^2 + x^29 - x^28*z0 + x^27*y*z0 - x^27*y - x^27*z0 + x^26*y*z0 + x^26*z0^2 - x^26*y - x^26*z0 + x^24*z0^2,
 -x^54*z0 - x^53*z0^2 - x^54 - x^53*z0 + x^52*y*z0 + x^51*y*z0^2 + x^53 + x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y + x^51*z0 + x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 - x^51 - x^50*y + x^50*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y + x^49*z0 + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^49 + x^48*y - x^48*z0 + x^47*y*z0 - x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 + x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y + x^46*z0 + x^44*y*z0^2 - x^46 + x^45*z0 + x^44*z0^2 - x^43*y*z0^2 - x^44*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^43*z0 - x^42*y*z0 + x^41*y*z0^2 - x^43 - x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 + x^42 - x^41*y - x^41*z0 + x^41 + x^40*z0 + x^39*z0^2 - x^39*y + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^39 - x^38*y + x^38*z0 + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y - x^36*z0 + x^34*y*z0^2 - x^36 - x^35*z0 - x^34*z0^2 - x^33*y*z0^2 - x^34*y - x^34*z0 + x^33*y*z0 - x^32*y*z0^2 + x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^32*y + x^32*z0 - x^32 - x^31*z0 - x^30*z0^2 + x^30*y - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^30 + x^29*y - x^29*z0 - x^28*y*z0 + x^28*z0^2 + x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 + x^28 - x^27*z0 + x^26*y*z0 + x^27 - x^26*y + x^24*y,
 x^54*z0 + x^53*z0^2 + x^54 - x^52*y*z0 - x^51*y*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*z0^2 + x^52 - x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^51 - x^50*y - x^50*z0 + x^49*z0^2 + x^48*y*z0^2 + x^49*y - x^49*z0 + x^48*z0^2 + x^47*y*z0^2 + x^49 + x^48*y - x^47*y*z0 + x^46*y*z0^2 - x^46*y*z0 - x^46*z0^2 + x^45*y*z0^2 + x^47 + x^46*y - x^45*y*z0 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 + x^43*y*z0^2 - x^45 - x^44*y - x^44*z0 - x^43*z0^2 - x^42*y*z0^2 + x^44 - x^43*y - x^43*z0 + x^42*y*z0 - x^41*y*z0^2 - x^42*z0 - x^41*y*z0 + x^41*z0^2 + x^42 + x^41*y + x^41 + x^39*y*z0 - x^39*z0^2 - x^40 - x^39*y - x^39*z0 - x^38*y*z0 + x^38*z0^2 - x^37*y*z0^2 + x^39 - x^38*y - x^37*y*z0 + x^37*z0^2 + x^38 - x^37*z0 + x^36*z0^2 + x^35*y*z0^2 + x^37 - x^36*y + x^36*z0 - x^35*y*z0 - x^34*y*z0^2 + x^35*y - x^35*z0 + x^34*z0^2 + x^33*y*z0^2 + x^34*y - x^33*y*z0 + x^32*y*z0^2 - x^33*z0 + x^32*y*z0 - x^32*z0^2 - x^33 - x^32*y - x^32 - x^30*y*z0 + x^30*z0^2 + x^31 + x^30*y + x^30*z0 + x^29*y*z0 - x^29*z0^2 + x^28*y*z0^2 - x^30 + x^29*y + x^28*y*z0 - x^28*z0^2 + x^29 + x^27*z0^2 - x^26*y*z0^2 + x^28 + x^27*z0 + x^26*y + x^26*z0 + x^24*y*z0,
 -x^54 - x^53*z0 + x^52*z0^2 - x^53 + x^52*y - x^52*z0 + x^51*y*z0 + x^51*z0^2 - x^50*y*z0^2 - x^52 + x^51*y - x^51*z0 + x^50*y*z0 + x^50*z0^2 - x^49*y*z0^2 + x^50*y + x^49*y*z0 + x^49*z0^2 - x^48*y*z0^2 - x^50 + x^49*y - x^49*z0 + x^48*y*z0 + x^47*y*z0^2 + x^47*z0^2 + x^46*y*z0^2 + x^48 - x^47*y + x^47*z0 - x^46*y*z0 + x^45*z0^2 + x^44*y*z0^2 - x^46 + x^45*y - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 - x^43*z0^2 - x^42*y*z0^2 - x^44 - x^43*y - x^43*z0 - x^42*y*z0 + x^42*z0^2 - x^41*y*z0^2 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^42 - x^41*z0 + x^40*z0^2 + x^39*y*z0^2 - x^41 - x^40*z0 + x^39*z0^2 + x^40 - x^39*y + x^39*z0 - x^38*y*z0 - x^38*z0^2 - x^37*y*z0^2 + x^39 + x^38*y + x^38*z0 + x^37*y*z0 + x^37*z0^2 - x^36*y*z0^2 - x^37*y - x^36*y*z0 + x^36*z0^2 + x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*y + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y + x^34*z0 + x^33*y*z0 + x^32*y*z0^2 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^33 + x^32*z0 - x^31*z0^2 - x^30*y*z0^2 + x^32 + x^31*z0 - x^30*z0^2 - x^31 + x^30*y - x^30*z0 + x^29*y*z0 + x^29*z0^2 + x^28*y*z0^2 - x^30 - x^29*y - x^29*z0 - x^28*y*z0 - x^28*z0^2 + x^27*y*z0^2 - x^29 + x^28*y - x^28*z0 + x^27*y*z0 + x^27*z0^2 + x^28 - x^27*y + x^27*z0 - x^26*y*z0 + x^26*z0^2 + x^27 + x^26*z0 + x^24*y*z0^2,
 x^55 - x^53*z0^2 - x^54 - x^53*y - x^53*z0 + x^51*y*z0^2 + x^53 + x^52*y + x^52*z0 + x^51*y*z0 - x^51*z0^2 + x^52 - x^51*y - x^51*z0 - x^50*y*z0 - x^50*z0^2 + x^49*y*z0^2 + x^51 + x^50*y + x^50*z0 + x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 - x^50 - x^49*y - x^49*z0 - x^48*z0^2 - x^47*y*z0^2 + x^48*y + x^48*z0 + x^47*y*z0 - x^46*y*z0^2 - x^48 + x^47*y - x^47*z0 - x^46*y*z0 + x^46*z0^2 - x^45*y*z0^2 - x^47 - x^46*y - x^46*z0 + x^45*y*z0 + x^44*y*z0^2 + x^46 + x^45*y + x^45*z0 + x^44*y*z0 + x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^44*z0 - x^43*y*z0 + x^43*z0^2 + x^42*y*z0^2 + x^43*y + x^41*y*z0^2 + x^43 + x^42*y + x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^42 - x^41*y - x^41*z0 + x^41 - x^40*y + x^40*z0 + x^39*z0^2 + x^39*y + x^39*z0 + x^38*y*z0 - x^38*z0^2 + x^37*y*z0^2 + x^38*y + x^37*y*z0 - x^37*z0^2 + x^38 + x^37*y + x^37*z0 + x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^37 + x^36*y + x^36*z0 + x^35*y*z0 + x^34*y*z0^2 - x^36 - x^35*y - x^35*z0 + x^34*y*z0 - x^34*z0^2 - x^33*y*z0^2 - x^32*y*z0^2 - x^34 - x^33*y - x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^33 + x^32*y + x^32*z0 - x^32 + x^31*y - x^31*z0 - x^30*z0^2 - x^30*y - x^30*z0 - x^29*y*z0 + x^29*z0^2 - x^28*y*z0^2 - x^29*y - x^28*y*z0 + x^28*z0^2 - x^28*y - x^27*y*z0 - x^27*z0^2 + x^26*y*z0^2 - x^27 - x^26*z0 + x^25,
 x^55 + x^54*z0 + x^54 - x^53*y - x^53*z0 - x^52*y*z0 + x^52*z0^2 + x^53 - x^52*y - x^52*z0 + x^51*y*z0 - x^51*z0^2 - x^50*y*z0^2 - x^52 - x^51*y + x^50*y*z0 + x^50*z0^2 + x^49*y*z0^2 + x^51 - x^50*z0 - x^49*y*z0 - x^49*z0^2 - x^48*y*z0^2 + x^48*y*z0 + x^48*z0^2 + x^48*y + x^48*z0 - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 + x^48 + x^47*z0 + x^46*z0^2 + x^45*y*z0^2 + x^47 - x^46*y - x^46*z0 + x^45*z0^2 - x^44*y*z0^2 + x^45*y - x^44*y*z0 - x^44*z0^2 - x^43*y*z0^2 + x^45 - x^44*y + x^43*y*z0 - x^43*z0^2 + x^42*y*z0^2 - x^44 - x^42*y*z0 - x^43 + x^42*y - x^42*z0 + x^41*y*z0 - x^41*z0^2 - x^40*y*z0^2 + x^42 - x^41*y - x^41*z0 + x^40*z0^2 - x^41 - x^39*z0^2 + x^39*y - x^39*z0 - x^38*z0^2 - x^37*y*z0^2 - x^38*y + x^38*z0 + x^37*y*z0 - x^36*y*z0^2 + x^38 - x^37*y - x^37*z0 - x^36*y*z0 - x^36*z0^2 - x^35*y*z0^2 + x^36*y + x^36*z0 - x^35*z0^2 - x^34*y*z0^2 + x^35*y - x^34*y*z0 + x^34*z0^2 - x^33*y*z0^2 + x^33*y*z0 + x^34 - x^33*y + x^33*z0 - x^32*y*z0 + x^32*z0^2 + x^31*y*z0^2 - x^33 + x^32*y + x^32*z0 - x^31*z0^2 + x^32 + x^30*z0^2 - x^30*y + x^30*z0 + x^29*z0^2 + x^28*y*z0^2 + x^29*y - x^29*z0 - x^28*y*z0 + x^27*y*z0^2 + x^28*y + x^28*z0 + x^27*y*z0 + x^26*y*z0^2 - x^28 - x^27 - x^26*y - x^26*z0 + x^25*z0^2,
 -x^55 - x^54*z0 + x^54 + x^53*y + x^53*z0 + x^52*y*z0 - x^52*z0^2 + x^53 - x^52*y - x^51*y*z0 + x^50*y*z0^2 - x^51*y - x^50*z0^2 - x^51 + x^50*y - x^50*z0 + x^49*y*z0 - x^49*z0^2 + x^48*y*z0^2 - x^50 + x^49*y + x^48*y*z0 - x^48*z0^2 - x^47*y*z0^2 - x^48*y - x^47*y*z0 - x^47*z0^2 - x^46*y*z0^2 - x^47*y - x^45*y*z0^2 - x^47 + x^46*y + x^45*y*z0 + x^45*z0^2 - x^44*y*z0^2 - x^46 - x^45*z0 + x^44*y*z0 + x^43*y*z0^2 - x^43*y*z0 + x^43*z0^2 - x^42*y*z0^2 - x^43*y + x^43*z0 - x^42*y*z0 + x^42*z0^2 + x^41*y*z0^2 - x^41*y*z0 + x^40*y*z0^2 + x^42 + x^41*y + x^41*z0 - x^40*z0^2 - x^40*z0 + x^40 + x^39*y + x^39*z0 - x^38*y*z0 + x^38*z0^2 + x^39 - x^38*y + x^38*z0 - x^37*y*z0 - x^37*z0^2 + x^36*y*z0^2 - x^38 - x^37*z0 - x^36*z0^2 - x^36*y + x^35*y*z0 - x^35*z0^2 - x^34*y*z0^2 + x^36 + x^35*z0 + x^34*y*z0 + x^33*y*z0^2 + x^35 + x^34*y - x^34*z0 + x^33*y*z0 - x^33*z0^2 - x^32*y*z0^2 + x^32*y*z0 - x^31*y*z0^2 - x^33 - x^32*y - x^32*z0 + x^31*z0^2 + x^31*z0 - x^31 - x^30*y - x^30*z0 + x^29*y*z0 - x^29*z0^2 - x^30 + x^29*y - x^29*z0 + x^28*y*z0 + x^28*z0^2 - x^27*y*z0^2 - x^29 + x^27*z0^2 - x^28 - x^27*y - x^27*z0 + x^26*y*z0 - x^26*z0^2 + x^25*y*z0^2 - x^27 + x^26*y - x^26*z0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.expansionat_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y

[?7h[?12l[?25h[?2004l[?7hy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t^2 + 2*t^3 + t^8 + t^9 + 2*t^14 + 2*t^15 + t^17 + 2*t^18 + 2*t^20 + 2*t^24 + 2*t^26 + t^27 + 2*t^29 + t^35 + 2*t^42 + t^47 + 2*t^48 + 2*t^51 + 2*t^53 + t^54 + 2*t^56 + 2*t^60 + 2*t^62 + t^68 + 2*t^74 + t^78 + t^81 + 2*t^83 + 2*t^87 + t^89 + 2*t^93 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [C.x*C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7lC.y], prec = 20)[?7h[?12l[?25h[?25l[?7l.y], prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: AS.pseudo_magical_element(threshold = 30)

[?7h[?12l[?25h[?2004l[?7h[-x^115 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^72*y*z0^2 + x^73*y + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y + x^57*y*z0^2 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^57 - x^55*y*z0 - x^56 + z0^2,
 -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^102 - x^100*y*z0 - x^101 + x^100*y + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^97*z0^2 + x^96*y*z0^2 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^92 - x^91*y + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 - x^84*z0 - x^82*y*z0^2 - x^83*y - x^82*y*z0 + x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y + x^79*y*z0^2 + x^81 + x^79*y*z0 + x^79*z0^2 + x^80 - x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^72 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y + x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 - x^55*y + y,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 - x^108*y*z0 + x^109 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y + x^104*y*z0 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^92*y + x^92*z0 + x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*y + x^86*z0 + x^85*y*z0 - x^86 - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 - x^83*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 - x^79 - x^77*y*z0 - x^76*y*z0^2 + x^78 - x^77*y - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^67*z0 - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^61 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + y*z0,
 x^115 + x^114*z0 - x^113*z0 + x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 + x^110*y*z0 - x^109*y*z0^2 - x^111 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*z0^2 - x^109 + x^108*y + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^104*z0^2 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^102*y - x^102*z0 + x^101*y - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^94*y*z0^2 - x^94*z0^2 - x^95 + x^94*z0 + x^93*y*z0 - x^94 - x^93*y + x^93*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*z0 - x^90*z0^2 + x^91 + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^87 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^84*y*z0 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^71*y*z0^2 - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^63*z0^2 - x^62*y*z0^2 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 + x^61*y - x^59*y*z0^2 - x^61 - x^60*y + x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 - x^57*z0 + x^56*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 + x^55*y + y*z0^2,
 -x^115 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^72*y*z0^2 + x^73*y + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y + x^57*y*z0^2 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^57 - x^55*y*z0 - x^56 + x*z0,
 x^115 - x^113*z0^2 - x^112*z0^2 + x^113 - x^112*y + x^110*y*z0^2 - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y + x^110 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*y - x^107*z0 + x^106*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y + x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^102*y + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 + x^100*y + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*y - x^96*y*z0^2 - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^93*y*z0 + x^93*z0^2 - x^94 - x^93*y - x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^88*y*z0 - x^89 - x^88*y - x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*z0^2 - x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y + x^75*y*z0 - x^74*y*z0^2 + x^75*y - x^75*z0 + x^73*y*z0^2 + x^75 + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^73*y + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*z0 + x^70*y*z0^2 + x^72 - x^71*y - x^70*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^70 + x^68*z0^2 + x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^67 + x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^65 - x^64*y - x^64*z0 - x^62*y*z0^2 - x^63*y + x^61*y*z0^2 + x^63 - x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 + x^57*y - x^56*y*z0 + x^55*y*z0^2 - x^56*y + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 - x^106*y*z0^2 - x^108 - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*z0 + x^104*y*z0^2 - x^106 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 + x^101*z0 + x^99*y*z0^2 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*z0 + x^96*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^94*z0^2 + x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*z0 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^81*y*z0 + x^80*y*z0^2 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 - x^76 + x^75*y + x^74*z0^2 + x^73*y*z0^2 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*y - x^62*z0 + x^61*y*z0 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^55*y*z0 - x^56 + x*y,
 -x^114 - x^113 + x^112*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*z0 - x^101*y*z0 - x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^93*y*z0^2 - x^94*y - x^93*y*z0 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*y*z0 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^85*y*z0^2 + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^82*y - x^81*y*z0 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*y - x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x*y*z0,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 + x^99 + x^98*y + x^98*z0 + x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*z0 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^91*y*z0 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 - x^79*y*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^65 - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x*y*z0^2,
 -x^115 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^72*y*z0^2 + x^73*y + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y + x^57*y*z0^2 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^57 - x^55*y*z0 - x^56 + x^2,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 + x^111 - x^110*y + x^110*z0 + x^110 + x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*z0 - x^104*y*z0 - x^103*y*z0^2 - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^101 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^98*z0^2 - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^94*y*z0 - x^95 + x^93*y*z0 - x^92*y*z0^2 + x^93*y - x^93*z0 + x^92*y*z0 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 + x^90*z0 + x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^86*y*z0 - x^86*z0^2 - x^87 + x^85*y*z0 - x^84*y*z0^2 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 - x^81*z0^2 - x^82 + x^81*y + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 - x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*z0 + x^78 - x^77*y - x^77*z0 - x^77 - x^76*y + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*y + x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^73*y - x^72*y*z0 + x^72*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^70*y + x^68*y*z0^2 + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^64*y - x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 + x^63*z0 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^58*y*z0 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 + x^55*y*z0 + x^2*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^107*y*z0 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*z0 - x^103*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 - x^99*y + x^98*y*z0 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*y - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*z0 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*y + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^92 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^91 + x^90*y + x^89*y + x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^83 + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*y*z0 + x^75*z0^2 + x^76 + x^74*y*z0 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^73*z0 + x^73 - x^72*y + x^72*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^66*y*z0^2 + x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y + x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*z0^2 - x^64 + x^63*y - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^2*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 - x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^95*y*z0^2 - x^97 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*z0^2 + x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 - x^88*z0^2 - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^85 - x^83*z0^2 - x^82*y*z0^2 - x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 + x^75*y*z0^2 + x^77 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^69*z0 - x^67*y*z0^2 + x^69 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 + x^64 + x^63*y - x^63*z0 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^60*y*z0 - x^61 - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 + x^2*y,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*y*z0 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^105*y*z0^2 + x^106*y - x^105*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^94*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^88*z0^2 + x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^69*y - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 + x^61*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 - x^58 + x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^2*y*z0,
 x^115 + x^114*z0 + x^114 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y - x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^103*y*z0^2 + x^105 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^101*z0 + x^100*z0^2 - x^101 + x^100*y + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^99 + x^96*y*z0^2 - x^98 - x^97*y - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*z0 - x^95*z0^2 - x^95*y - x^94*y*z0 - x^93*y*z0^2 + x^95 - x^94*y + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 - x^83*y*z0 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*z0^2 + x^82 - x^81*y + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*z0^2 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^72*y - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y + x^65*y*z0^2 - x^67 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 - x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*z0 - x^59*y - x^59*z0 - x^58*z0^2 + x^58*y + x^58*z0 - x^57*y*z0 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^55*y + x^2*y*z0^2,
 -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^102 - x^100*y*z0 - x^101 + x^100*y + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^97*z0^2 + x^96*y*z0^2 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^92 - x^91*y + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 - x^84*z0 - x^82*y*z0^2 - x^83*y - x^82*y*z0 + x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y + x^79*y*z0^2 + x^81 + x^79*y*z0 + x^79*z0^2 + x^80 - x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^72 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y + x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^3,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 - x^108*y*z0 + x^109 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y + x^104*y*z0 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^92*y + x^92*z0 + x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*y + x^86*z0 + x^85*y*z0 - x^86 - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 - x^83*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 - x^79 - x^77*y*z0 - x^76*y*z0^2 + x^78 - x^77*y - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^67*z0 - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^61 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^3*z0,
 x^115 + x^114*z0 - x^113*z0 + x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 + x^110*y*z0 - x^109*y*z0^2 - x^111 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*z0^2 - x^109 + x^108*y + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^104*z0^2 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^102*y - x^102*z0 + x^101*y - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^94*y*z0^2 - x^94*z0^2 - x^95 + x^94*z0 + x^93*y*z0 - x^94 - x^93*y + x^93*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*z0 - x^90*z0^2 + x^91 + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^87 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^84*y*z0 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^71*y*z0^2 - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^63*z0^2 - x^62*y*z0^2 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 + x^61*y - x^59*y*z0^2 - x^61 - x^60*y + x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 - x^57*z0 + x^56*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 + x^55*y + x^3*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 - x^109*y*z0 - x^108*y*z0^2 + x^108*y*z0 + x^109 + x^108*y - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 + x^104 + x^103*z0 - x^103 - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*y - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*z0^2 + x^81 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^77*y - x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y + x^67*z0^2 - x^66*y*z0^2 - x^67*y - x^65*y*z0^2 - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^64*y*z0 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^55*y*z0^2 + x^56*y + x^3*y,
 -x^115 - x^114*z0 - x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^107*y*z0^2 + x^109 - x^108*y + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^97*y*z0 - x^97*z0^2 + x^98 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^95*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*z0^2 - x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^75 - x^73*y*z0 + x^73*z0^2 + x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y + x^67*y*z0^2 - x^69 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^65*y + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^63*y + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56 + x^55*y + x^3*y*z0,
 x^115 - x^113*z0^2 - x^113*z0 - x^112*y + x^110*y*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 - x^110*z0 + x^110 + x^109*y + x^108*y*z0 - x^107*y*z0^2 - x^108*y + x^107*y*z0 + x^108 + x^107*y + x^107*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 - x^98*y*z0 + x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^96 + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*y - x^90*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^89 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y + x^86*y*z0 + x^85*y*z0^2 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 + x^84 - x^83*y + x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^81*y - x^81*z0 + x^80*y*z0 + x^81 + x^80*y - x^79*y*z0 + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*y + x^75*y*z0 - x^74*y*z0^2 + x^76 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 + x^73 - x^72*y - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*z0 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^61*z0^2 + x^62 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y + x^3*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 - x^106*y*z0^2 - x^108 - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*z0 + x^104*y*z0^2 - x^106 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 + x^101*z0 + x^99*y*z0^2 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*z0 + x^96*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^94*z0^2 + x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*z0 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^81*y*z0 + x^80*y*z0^2 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 - x^76 + x^75*y + x^74*z0^2 + x^73*y*z0^2 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*y - x^62*z0 + x^61*y*z0 + x^62 - x^61*y - x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^55*y*z0 - x^56 + x^4,
 -x^114 - x^113 + x^112*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*z0 - x^101*y*z0 - x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^93*y*z0^2 - x^94*y - x^93*y*z0 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*y*z0 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^85*y*z0^2 + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^82*y - x^81*y*z0 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*y - x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^4*z0,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 + x^99 + x^98*y + x^98*z0 + x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*z0 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^91*y*z0 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 - x^79*y*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^65 - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x^4*z0^2,
 x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 - x^99*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*y + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^93 + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^88*y*z0 + x^88*z0^2 - x^89 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^82*z0 - x^81*z0^2 + x^82 - x^81*y - x^81*z0 + x^81 + x^79*y*z0 - x^79*z0^2 + x^80 - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 + x^72*z0 - x^71*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*z0^2 + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^65*y*z0 - x^64*y*z0^2 - x^66 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0 + x^63*z0^2 - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 + x^56*y*z0^2 + x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 + x^55*y + x^4*y,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y - x^110*z0^2 - x^111 - x^109*z0^2 + x^110 - x^109*y + x^109*z0 + x^107*y*z0^2 - x^109 + x^108*y + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y - x^101*y*z0 + x^101*z0^2 + x^101*y + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*z0^2 - x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y + x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y + x^78*y*z0 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77*z0 + x^76*y*z0 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^73*y*z0^2 - x^75 - x^73*z0^2 - x^74 + x^72*y*z0 + x^73 - x^72*y - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0 - x^64*z0^2 - x^65 + x^64*y - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*z0^2 + x^62*y + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^4*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^102*y*z0 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^98*y*z0 - x^98*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^98 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^95 + x^94*z0 + x^92*y*z0^2 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*z0 - x^86*y*z0 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 - x^85 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^83 + x^82*y + x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 - x^81 + x^79*y*z0 + x^80 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^77*y*z0 - x^76*y*z0^2 - x^77*y - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^77 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 + x^73 - x^72*z0 - x^70*y*z0^2 + x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 - x^69*z0^2 - x^70 + x^69*y - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*z0^2 - x^66 + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^62*y + x^62*z0 + x^60*y*z0^2 - x^61*y + x^60*y*z0 - x^60*z0^2 - x^61 + x^60*z0 + x^59*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y + x^57*y*z0 + x^58 - x^57*y - x^57*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 + x^56 + x^55*y + x^4*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 - x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^95*y*z0^2 - x^97 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*z0^2 + x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 - x^88*z0^2 - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^85 - x^83*z0^2 - x^82*y*z0^2 - x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 + x^75*y*z0^2 + x^77 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^69*z0 - x^67*y*z0^2 + x^69 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 + x^64 + x^63*y - x^63*z0 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^60*y*z0 - x^61 - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 + x^5,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*y*z0 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^105*y*z0^2 + x^106*y - x^105*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^94*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^88*z0^2 + x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^69*y - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 + x^61*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 - x^58 + x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^5*z0,
 -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^111*y*z0 + x^111*z0^2 + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^106*y*z0^2 - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^102 + x^100*y*z0 + x^101 - x^99*y*z0 - x^99*z0^2 + x^100 - x^99*y + x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 + x^97*y + x^96*y*z0 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^95 + x^94*y - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*z0 - x^93 + x^92*y + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*z0 + x^89*y*z0^2 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^86*y*z0 + x^86*z0^2 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 + x^81*y*z0 - x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^76 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*y - x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 - x^58*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56 - x^55*y + x^5*z0^2,
 -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y - x^109*y*z0 - x^109*z0^2 + x^110 + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*z0^2 - x^106*y - x^105*y*z0 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*y - x^94*y*z0^2 + x^96 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y - x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^88*z0^2 - x^89 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^85*y - x^85*z0 - x^84*y*z0 + x^85 - x^84*z0 - x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 - x^70*z0^2 + x^71 + x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 + x^65 - x^64*y + x^64*z0 + x^64 + x^63*y + x^63*z0 + x^63 - x^62*z0 + x^62 - x^61*y + x^60*z0^2 + x^61 + x^60*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^57*y*z0^2 + x^59 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^56*y - x^56*z0 + x^56 + x^5*y,
 -x^115 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*y + x^102*y*z0 + x^102*z0^2 + x^103 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^98*y*z0 - x^97*y*z0^2 - x^98*z0 + x^97*y*z0 + x^98 + x^97*y - x^97*z0 + x^96*y*z0 - x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^96 - x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^91 - x^90*y - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y - x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*y - x^79*z0^2 + x^80 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*z0^2 + x^76*y - x^75*z0^2 + x^76 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 - x^72*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^60*y*z0^2 + x^62 + x^61*y - x^60*y*z0 + x^59*y*z0^2 + x^60*y - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 - x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^5*y*z0,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*y*z0 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^100 - x^99*y - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*z0^2 - x^98 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*y*z0 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 - x^82 - x^81*y - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*z0^2 - x^75*y*z0^2 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 + x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^73 + x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 - x^56*z0 + x^55*y + x^5*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 - x^109*y*z0 - x^108*y*z0^2 + x^108*y*z0 + x^109 + x^108*y - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 + x^104 + x^103*z0 - x^103 - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*z0^2 - x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*y - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*z0^2 + x^81 + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^77*y - x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y + x^67*z0^2 - x^66*y*z0^2 - x^67*y - x^65*y*z0^2 - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^64*y*z0 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^55*y*z0^2 + x^56*y + x^6,
 -x^115 + x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^107*y + x^107*z0 - x^106*z0^2 + x^107 + x^106*z0 + x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y - x^101*y*z0^2 + x^103 - x^102*z0 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 - x^95*y*z0^2 - x^97 + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 - x^87*y - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 + x^84*y*z0 - x^84*z0^2 + x^84*y + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^81*y*z0 - x^81*z0^2 + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*y*z0 + x^73*z0^2 + x^73*y - x^72*z0^2 - x^73 - x^72*y - x^71*y*z0 - x^72 - x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^66*z0^2 + x^65*y*z0^2 + x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^64 + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*y + x^58*z0 - x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 + x^56 + x^6*z0,
 -x^114*z0 - x^113*z0^2 + x^114 + x^113 + x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^110 + x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^108*z0 + x^107*y*z0 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 - x^100*z0^2 - x^100*y + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*y*z0 - x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^91 + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^82 - x^81*y + x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 - x^78*y - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*z0 + x^76*y*z0 - x^76*y + x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 + x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^73 - x^72*z0 + x^71*y*z0 - x^72 - x^71*y - x^70*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^67*y + x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*y - x^65*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^60 - x^59*y - x^59*z0 + x^58*y*z0 - x^58*y - x^58*z0 + x^57*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^6*z0^2,
 -x^115 + x^113*z0^2 - x^114 - x^113 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 - x^105*y*z0^2 + x^105*y*z0 - x^106 + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^103 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^97*y*z0 + x^97*z0^2 + x^98 - x^97*y + x^96*y*z0 - x^96*z0^2 + x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^94 - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*y - x^92*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*z0^2 + x^89 + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^82*y*z0 - x^82*z0 - x^80*y*z0^2 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*z0^2 - x^80 - x^78*z0^2 - x^79 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*z0 - x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^70 - x^69*y + x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 + x^65*z0^2 + x^66 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^61*y*z0^2 + x^62*y - x^62*z0 + x^61*y*z0 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^60 + x^59*y - x^59*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 - x^58 - x^57*y - x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^6*y,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*z0^2 - x^111 - x^110*y + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^101*z0^2 - x^102 - x^101*y - x^100*y*z0 - x^99*y*z0^2 + x^100*z0 + x^98*y*z0^2 - x^99*y + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^90*y - x^90*z0 - x^89*z0^2 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^83 - x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^79*y*z0 + x^80 + x^79*y + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 + x^76 - x^75*y + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^71*y + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 + x^69 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 + x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^59 - x^57*y*z0 + x^58 - x^57*y - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^6*y*z0,
 x^115 + x^114*z0 - x^114 - x^113*z0 - x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 + x^111*y + x^110*y*z0 + x^110*z0^2 - x^111 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 + x^101*y - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^95*z0^2 - x^96 - x^95*y + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 - x^83*y*z0 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^75 - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y - x^72*y*z0 + x^72*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y - x^69*y*z0 + x^69*z0^2 + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*z0^2 - x^67*y - x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*z0 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y + x^56*z0 + x^56 - x^55*y + x^6*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 + x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 + x^107*z0 + x^106*z0^2 - x^107 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 - x^105*y + x^105*z0 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^98*y*z0^2 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*z0 + x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^75 - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^71*y - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y + x^64*y*z0 - x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^62 - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^7,
 -x^115 - x^114*z0 - x^113*z0 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^106*y*z0 - x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^103*y*z0^2 + x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 + x^71*y + x^71*z0 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 + x^69*y + x^68*z0^2 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^65*y*z0^2 + x^66*y - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 - x^63*y*z0^2 - x^64*z0 - x^63*z0^2 + x^64 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*y*z0 + x^59 + x^58*y - x^58*z0 - x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^55*y*z0^2 + x^57 - x^56*z0 + x^56 + x^55*y + x^7*z0,
 -x^115 - x^114*z0 - x^114 + x^113 + x^112*y + x^111*y*z0 + x^111*y - x^111*z0 + x^110*z0^2 - x^110*y - x^109*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^105*y*z0 - x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 + x^101*y - x^101*z0 + x^100*y*z0 + x^99*y*z0^2 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^95*y*z0^2 - x^97 + x^96*y - x^95*z0^2 - x^96 + x^95*y + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 - x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^87*y + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y - x^85*z0^2 - x^86 + x^85*z0 + x^84*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^81*z0^2 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^79*y*z0 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*y + x^75*y*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*z0^2 + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^63*z0 + x^62*y*z0 + x^63 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^60 + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56*z0 + x^56 + x^55*y + x^7*z0^2,
 -x^113*z0 + x^112*z0^2 - x^112*z0 + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 - x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^106*z0 + x^105*y*z0 + x^106 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 - x^102*z0^2 - x^102*y + x^102*z0 - x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^99*y*z0 + x^98*y*z0 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^91*y*z0 - x^90*y*z0 - x^90*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^78*y + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y + x^73*y*z0 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0 - x^69*z0^2 - x^70 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*z0 - x^63*y*z0^2 + x^65 - x^64*y - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^63 - x^62*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 - x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^7*y,
 -x^114*z0 - x^113*z0^2 + x^114 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^107*y*z0^2 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*z0 - x^102*y*z0^2 - x^104 - x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^93*y - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 + x^91*z0 + x^90*z0^2 + x^89*y*z0^2 - x^89*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 - x^80 + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^77*z0^2 + x^76*y*z0^2 + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^73*z0 - x^71*y*z0^2 + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 + x^66 + x^65*y - x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 - x^61 + x^60*y - x^59*z0^2 - x^58*y*z0^2 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^59 - x^57*y*z0 - x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^7*y*z0,
 x^114*z0 + x^113*z0^2 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^105*z0 - x^103*y*z0^2 + x^105 + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^103*y - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*z0^2 - x^100 - x^99*y + x^98*y*z0 - x^97*y*z0^2 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*z0 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 + x^85*y*z0^2 + x^86*z0 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^78 - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^70*y*z0^2 - x^71*y - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^64*z0^2 - x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*z0^2 - x^60 + x^59*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*z0 - x^56 + x^7*y*z0^2,
 x^115 - x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^109 + x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*y - x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^102*z0 + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 - x^99*y*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 - x^98*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^94*y*z0 - x^95 - x^94*y - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 + x^91*z0^2 - x^92 + x^91*y - x^91*z0 - x^89*y*z0^2 - x^91 + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79 - x^78*y - x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^74*y*z0 - x^74*z0^2 + x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*y + x^60*z0 - x^59*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^56*y + x^55*y*z0 - x^55*y + x^8,
 x^114*z0 + x^113*z0^2 - x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^111*z0 + x^110*z0^2 - x^111 + x^110*y - x^109*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*z0 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*z0 + x^101*y*z0^2 + x^103 + x^102*y + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 + x^99*y*z0 + x^100 + x^99*y + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^94 - x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^88*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^81 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y + x^75*z0 - x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^71 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^67 - x^66*y - x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0 - x^57*z0^2 + x^58 - x^57*y + x^57*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^8*z0,
 -x^115 - x^114*z0 + x^113*z0 - x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^110*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 - x^106*y + x^106*z0 - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^103 - x^102*y - x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^100 - x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y + x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^92*z0^2 - x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^87*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^82 - x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77*y - x^76*z0^2 - x^75*y*z0^2 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^74*y*z0 - x^74*z0^2 - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 + x^70*z0 + x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 - x^61 + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^55*y*z0 - x^55*y + x^8*z0^2,
 -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^107 - x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^102*y*z0^2 + x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^99*z0^2 - x^99*y - x^98*y*z0 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y - x^92*z0 - x^91*y*z0 - x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*y + x^86*z0^2 - x^87 + x^86*y + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^83 - x^82*y - x^82*z0 + x^80*y*z0^2 - x^82 + x^81*y - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 - x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 - x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 + x^73 + x^71*z0^2 - x^70*y*z0^2 + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^69*y - x^68*y*z0 - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^68 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^62*y*z0 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^61*y - x^61*z0 - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^57*z0 - x^56*z0^2 - x^55*y*z0^2 - x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^8*y,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 + x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^100*z0^2 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*y - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^92*y*z0 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^89*z0 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*z0^2 + x^87*y + x^87*z0 + x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*y*z0 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 + x^79*y*z0^2 - x^80*y - x^80*z0 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^74*y - x^74*z0 - x^73*z0^2 + x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 - x^68*y + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 - x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^61*y*z0 - x^62 - x^61*y - x^61*z0 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^60 + x^59*y + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^8*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 - x^111*y + x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y + x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^98*y*z0 + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 - x^94 - x^93*z0 - x^91*y*z0^2 - x^93 + x^92*z0 + x^91*z0^2 + x^91*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 + x^89 + x^88*y + x^88*z0 + x^86*y*z0^2 - x^87*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^74*y*z0 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^69*y*z0 + x^70 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*z0 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 + x^56 + x^8*y*z0^2,
 -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^109*y - x^108*y*z0 - x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^108 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*z0 + x^105 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 + x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^93*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^87*y*z0 + x^87*z0^2 - x^87*y - x^86*y*z0 + x^86*y + x^86*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^82*z0 - x^80*y*z0^2 - x^82 - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y + x^75*y*z0 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^71 - x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*z0 - x^63*z0^2 - x^64 + x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^9,
 -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*z0 + x^96*z0^2 - x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^89*y*z0^2 - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 + x^87*y*z0 - x^87*z0^2 - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*y - x^86 + x^84*z0^2 + x^85 + x^83*y*z0 - x^83*z0^2 - x^84 - x^83*y + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^80*y - x^80*z0 - x^79*z0^2 - x^80 + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*z0 + x^74*z0^2 - x^74*y - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 + x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*z0 + x^65*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^65 - x^64*y + x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^61*y*z0 + x^61*z0^2 - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^60*y + x^60*z0 + x^58*y*z0^2 - x^59*y + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^57*y*z0 - x^57*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^9*z0,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^111 - x^110*z0 + x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 + x^88*z0^2 + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^78*y*z0^2 + x^79*y + x^79*z0 - x^79 - x^78*y + x^78*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 + x^75 - x^74*y - x^73*y*z0 - x^72*y*z0^2 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^71*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^67*y*z0 + x^67*z0^2 + x^68 + x^67*y + x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 + x^65 + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^63 + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*y - x^58*y*z0 + x^57*y*z0^2 - x^59 - x^57*y*z0 - x^58 - x^57*y + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^9*z0^2,
 x^115 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^91 - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*z0^2 - x^87 + x^86*y - x^85*y*z0 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^85 + x^83*y*z0 + x^83*z0^2 - x^84 - x^83*y + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 - x^81*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^78 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*z0 - x^70*z0^2 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 + x^65*z0^2 + x^66 + x^64*y*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^55*y*z0^2 + x^57 - x^55*y + x^9*y,
 -x^115 + x^113*z0^2 - x^113*z0 + x^112*y - x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*z0 + x^110*y*z0 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 + x^105*y - x^104*y*z0 + x^104*z0^2 + x^105 + x^104*y - x^103*z0^2 - x^102*y*z0^2 - x^103*z0 - x^102*z0^2 + x^103 + x^102*y - x^102 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^99*y*z0 + x^99*z0^2 + x^100 - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y - x^93*y*z0^2 + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 + x^91*y*z0^2 + x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^87*y - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^83*y*z0 + x^84 + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^78*y*z0^2 - x^80 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^74 + x^72*y*z0 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^72 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^66*y + x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*z0 - x^65 - x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^62*z0^2 + x^63 - x^62*y + x^61*y*z0 + x^62 + x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^60 - x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^57*y*z0 + x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^9*y*z0,
 -x^115 - x^114*z0 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 + x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^107*y*z0 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*z0^2 - x^103 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^97 + x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^91*y*z0 - x^90*y*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y - x^88*y*z0 + x^89 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^86*z0^2 + x^87 - x^86*y + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^81*y*z0 + x^80*y*z0^2 + x^81*y + x^80*z0^2 - x^80*y - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 - x^78*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 - x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 - x^70*y*z0^2 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^67 + x^66*y + x^66*z0 + x^64*y*z0^2 + x^66 + x^65*z0 + x^64*y*z0 - x^65 + x^64*y + x^64*z0 - x^63*z0^2 + x^63*y - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^61*z0 + x^61 + x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 - x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^56*y - x^55*y*z0 - x^56 + x^55*y + x^9*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^109 + x^108*y - x^108*z0 + x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*z0 + x^105*y*z0^2 - x^107 + x^106*z0 + x^104*y*z0^2 + x^105*y + x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 - x^96 + x^95*z0 - x^94*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^92*y - x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^87*y - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 + x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 + x^83 + x^82*y + x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^79*y*z0 + x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^79 + x^78*y - x^78*z0 + x^76*y*z0^2 - x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*z0^2 - x^75*y - x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^72*y*z0 + x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^69*z0^2 - x^69*y - x^69*z0 + x^69 - x^68*y - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 + x^64 + x^63*y - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^59*y*z0^2 + x^61 + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*z0 + x^58*y - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^55*y*z0 - x^56 - x^55*y + x^10,
 x^115 - x^113*z0^2 + x^114 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*z0^2 - x^109*y*z0^2 - x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^109*y - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*z0^2 - x^104 - x^102*y*z0 + x^103 - x^102*y - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^101 - x^100*y - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 - x^99 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^94*y*z0 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*y - x^93*z0 + x^92*y*z0 + x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^90*y*z0 - x^90*z0^2 + x^91 - x^90*y + x^88*y*z0^2 - x^90 + x^89*y - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y + x^84*z0^2 + x^85 - x^84*y + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^81*y*z0 + x^82 + x^81*z0 - x^80*y*z0 + x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^78 + x^77*y - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y - x^75*y*z0 - x^74*y*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*z0 + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^65*y + x^64*y*z0 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^58 + x^57*y + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y + x^10*z0,
 x^115 - x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 + x^109 + x^108*z0 - x^107*y*z0 + x^107*z0 + x^106*z0^2 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y - x^98*y*z0 - x^97*y*z0^2 - x^99 + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*z0^2 + x^97 - x^96*y - x^95*y*z0 - x^95*z0^2 - x^96 + x^95*y + x^94*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y + x^88*z0 - x^88 - x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 - x^85 - x^84*y + x^83*z0^2 + x^83*y + x^82*z0^2 + x^83 + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y + x^81*z0 - x^79*y*z0^2 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^79*z0 + x^78*y*z0 - x^79 + x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y + x^74 + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*z0 - x^67*y*z0^2 + x^69 - x^68*y + x^67*z0^2 - x^66*y*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*z0^2 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*z0 + x^61*y*z0^2 - x^63 + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 - x^55*y + x^10*z0^2,
 -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 - x^113 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^104*y*z0 - x^103*y*z0^2 - x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^103*y - x^102*z0^2 + x^103 - x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^95 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*z0^2 - x^93 - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 - x^88 - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^81*y*z0 + x^81*z0^2 + x^81*y - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y + x^72*y + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67 - x^66*y - x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^10*y,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*y + x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 - x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^99 + x^97*z0^2 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^97 + x^95*z0^2 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^94 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^87*y*z0 + x^87*z0^2 - x^87*y + x^86*y*z0 - x^86*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 + x^78 + x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^75*y + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^72*y*z0 + x^72*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^72 - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67 - x^66*y + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 + x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 + x^57*y*z0^2 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 + x^57*z0 - x^56*y*z0 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^10*y*z0,
 -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 + x^111*z0^2 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103 + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 + x^100*y*z0 + x^101 + x^100*y + x^100*z0 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 + x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^95 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*z0 - x^88*z0^2 - x^87*y*z0^2 + x^87*y*z0 + x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^84*z0^2 - x^83*y*z0^2 - x^84*y + x^83*z0^2 + x^84 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*y - x^79*z0^2 + x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*y + x^77*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 + x^73*y*z0^2 - x^75 + x^73*z0^2 + x^74 + x^72*y*z0 - x^72*z0^2 - x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^71 - x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^64 - x^62*z0^2 - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^61 + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*z0 + x^56 - x^55*y + x^10*y*z0^2,
 x^114 - x^112*z0^2 - x^113 - x^112 - x^111*y + x^111*z0 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*z0^2 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^106 + x^105*y + x^105*z0 + x^103*y*z0^2 + x^103*z0^2 - x^104 + x^103*y - x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 + x^100*y*z0^2 + x^102 + x^100*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 + x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*y - x^94*z0 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^93 + x^91*y*z0 + x^90*y*z0^2 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 + x^88*y*z0 - x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 - x^88 - x^87*y - x^87*z0 - x^86*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^80*y*z0^2 + x^82 + x^81*y - x^80*y*z0 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^67 + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^64 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y - x^61*z0^2 - x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^60*z0 - x^58*y*z0^2 + x^60 + x^59*z0 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^56 + x^55*y + x^11,
 x^115 + x^114*z0 - x^114 + x^113*z0 + x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*z0 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^107 + x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^99*y + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^98 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^91*y*z0^2 - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^89*z0 - x^88*y*z0 + x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 - x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 + x^84 + x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^80 + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 + x^76*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*z0 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*z0^2 + x^72*y + x^72*z0 + x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^68*y*z0 + x^69 - x^68*z0 + x^67*y*z0 + x^67*y - x^67*z0 + x^66*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^11*z0,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^101*y*z0^2 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^99 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^97 + x^96*y - x^95*y*z0 + x^95*z0^2 + x^96 - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*y + x^78*y*z0 + x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^76*y*z0^2 - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^76*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73 - x^72*y + x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 + x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^11*z0^2,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^109*y*z0 + x^108*y*z0^2 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*z0^2 - x^108 - x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^104*y - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^100*y*z0^2 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*y + x^91*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^88*y*z0^2 - x^90 + x^89*z0 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 - x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^84*y - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 + x^81*z0^2 + x^80*y*z0^2 + x^81*y - x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^76 + x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*z0 - x^72*y*z0^2 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^70*y + x^70*z0 + x^69*z0^2 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^55*y*z0 + x^56 + x^55*y + x^11*y,
 -x^114 - x^113*z0 - x^112*z0 + x^111*z0^2 + x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^105*y + x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^103*y*z0 - x^102*y*z0^2 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^98*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^86*y - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^79*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*z0 - x^73*y*z0^2 + x^74*y - x^74*z0 - x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^69*z0^2 + x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^63 - x^62*y + x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*y + x^58*y*z0 - x^58*z0^2 - x^59 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^56 - x^55*y + x^11*y*z0,
 x^115 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^112*y + x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 + x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*y - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 + x^100 - x^99*z0 + x^98*y*z0 + x^99 + x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 - x^94*y - x^94*z0 - x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^92*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^88*z0 - x^87*y*z0 + x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y - x^84*y*z0^2 + x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 + x^82*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y - x^80*y*z0 + x^79*y*z0^2 - x^80*y - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y + x^72*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^67*y*z0 - x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y - x^64*y*z0 + x^64*z0^2 - x^65 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^60 + x^58*y*z0 + x^58*z0^2 + x^59 - x^57*y*z0 - x^58 + x^57*y - x^57*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 - x^55*y + x^11*y*z0^2,
 -x^115 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 - x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 + x^102*y*z0^2 - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^101 - x^100*y - x^100*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*y - x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 + x^90*y*z0^2 - x^90*y*z0 - x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^86*y + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^80*y*z0 - x^80*z0^2 + x^80*y + x^80*z0 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^74*y - x^74*z0 - x^74 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y - x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^61*y*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y + x^60 - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0 + x^12,
 x^115 - x^114*z0 + x^113*z0^2 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^106*y - x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^105 - x^104*y - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y + x^101*y*z0^2 + x^103 + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^94*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^91*y*z0 - x^90*y*z0^2 + x^90*y*z0 + x^90*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^89*y + x^88*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*y*z0 + x^86*z0^2 + x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*z0^2 + x^77 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y - x^68*z0^2 + x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^68 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*z0 + x^66 - x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^61*y*z0 + x^61*z0^2 + x^62 + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^58*z0^2 - x^59 + x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^57*z0 + x^56*z0^2 + x^56 + x^55*y + x^12*z0,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^109*y - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^107*y*z0 - x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^104*y + x^104*z0 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 - x^97 + x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y - x^85*y*z0 - x^84*y*z0^2 + x^85*y - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^82*y*z0^2 + x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^80*y*z0^2 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*z0^2 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*y + x^73 - x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^59*z0^2 + x^58*y*z0^2 - x^58*y + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^12*z0^2,
 x^115 + x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^112 - x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*y - x^109*z0 + x^109 + x^107*y*z0 - x^108 - x^107*y + x^106*z0^2 + x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^101 - x^99*y*z0 + x^99*z0^2 + x^100 - x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^98*y + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 - x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 + x^91 - x^90*y - x^90*z0 - x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 + x^83*y*z0 + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^78*y*z0 + x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*z0 - x^77 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*y + x^75*z0 + x^73*y*z0 + x^73*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^71*z0^2 + x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*z0^2 + x^70 - x^69*y + x^69*z0 + x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y + x^65*y*z0^2 - x^67 - x^65*y*z0 + x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^61*z0 + x^60*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^58*y*z0 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*z0^2 - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^12*y,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 + x^104*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*z0 + x^101*z0^2 + x^102 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^97 - x^96*y + x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*y - x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^83*y + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^82*y + x^81*y - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 + x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*z0 + x^74*y*z0 - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^71 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^61 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y + x^58*z0 + x^58 + x^56*y*z0 + x^55*y*z0^2 - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^12*y*z0,
 -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 - x^108*y*z0^2 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^108 - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*y*z0 + x^103*y*z0^2 + x^104*y - x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 + x^99*y - x^99*z0 - x^98*y + x^97*y*z0 + x^98 - x^97*y - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*z0^2 + x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 + x^85*y*z0 - x^86 - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y + x^82*y*z0 - x^83 - x^82*z0 - x^81*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^78 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 + x^65*y*z0^2 + x^67 - x^66*y + x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^63 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^60*z0^2 + x^59*y*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*z0 - x^56*z0^2 + x^56*y - x^55*y*z0 - x^56 - x^55*y + x^12*y*z0^2,
 -x^115 - x^114*z0 + x^114 - x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^106*y*z0^2 + x^107*y - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^99*y - x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 + x^96*y - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^91*y*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 + x^80*y*z0 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y*z0 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*y - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 - x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^61 - x^60*y + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^59 - x^58*z0 - x^57*y*z0 + x^58 + x^57*y - x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^13,
 x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 - x^109*y - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^103 - x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^99*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^97*y*z0 + x^96*y*z0^2 + x^96*y*z0 - x^96*z0^2 - x^96*y - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^88 + x^86*y*z0 + x^86*z0^2 - x^87 - x^86*z0 - x^85*z0^2 - x^86 - x^85*y + x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^78 - x^76*y*z0 - x^76*z0^2 + x^77 + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^75*z0 - x^74*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 - x^70 - x^68*y*z0 - x^68*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 + x^63*y - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^62*y - x^62*z0 + x^62 + x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^59*y + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^13*z0,
 x^115 - x^113*z0^2 - x^113*z0 - x^112*z0^2 - x^113 - x^112*y - x^111*z0^2 + x^110*y*z0^2 + x^112 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 + x^108*y*z0^2 - x^109*y - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^108 - x^107*y - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*z0^2 - x^106 + x^104*y*z0 - x^104*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y + x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y - x^100*y*z0 - x^101 - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 + x^96*z0^2 + x^97 + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*z0^2 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^88*z0 - x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^83 - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y - x^78 - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^76*y + x^76*z0 + x^74*y*z0^2 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 + x^68 - x^67*y - x^65*y*z0^2 + x^67 + x^66*y + x^65*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^64*y + x^64*z0 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*y*z0 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^13*z0^2,
 x^114*z0 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^107*y*z0 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 - x^105 + x^104*y + x^104*z0 - x^103*y + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^102 - x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^99*y*z0 - x^99*z0^2 - x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 - x^97*z0^2 - x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^86*y*z0^2 + x^88 + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^79*y + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^75*y - x^75 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*z0 + x^71*y*z0 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^68*y - x^67*y*z0 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^67 - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 - x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^13*y,
 x^115 - x^113*z0^2 + x^114 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 - x^107 + x^106*y - x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*z0 - x^98*y*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^93*y + x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 + x^92 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^82*z0 - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y + x^77*y*z0 - x^76*y*z0^2 + x^77*z0 + x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*y - x^71*z0 + x^69*y*z0 + x^69*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^68*y - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^65*y - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^62 + x^61*y - x^61*z0 + x^61 + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^55*y + x^13*y*z0,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 - x^107*y*z0 - x^108 - x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^102*y*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 - x^102 - x^101*y + x^100*y*z0 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*y - x^95*z0 - x^94*y*z0 - x^95 + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*z0^2 + x^90 + x^89*z0 + x^88*z0^2 + x^88*y - x^87*y*z0 + x^88 - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*z0 - x^84 - x^83*y + x^83*z0 - x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*z0 - x^76 + x^75*y + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^73*y*z0 + x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^70*y*z0^2 + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 + x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y + x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*z0^2 - x^56*y - x^55*y*z0 + x^56 + x^13*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0 + x^110 + x^109*y + x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^107*z0^2 - x^108 + x^107*y - x^107*z0 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105 + x^104*y + x^103*z0^2 - x^102*y*z0^2 + x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 + x^97*z0^2 + x^98 + x^97*y - x^96*y*z0 + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 + x^94*y*z0 + x^93*y*z0^2 + x^93*y*z0 + x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*z0^2 - x^89 - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 - x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 - x^86 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 + x^79*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^64*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^62*z0^2 + x^63 - x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*z0^2 - x^58 - x^57*y - x^57*z0 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 - x^56 + x^55*y + x^14,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*z0 - x^108*y*z0^2 + x^110 + x^109*y + x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*z0 + x^95*y*z0 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 - x^93*y*z0 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^90*z0^2 - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*z0^2 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^82*z0 + x^81*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^79 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^74*z0 + x^73*y*z0 + x^74 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*z0^2 + x^67*z0 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^65*z0 + x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*y - x^63*z0 + x^62*y*z0 - x^63 + x^62*y - x^62*z0 + x^61*z0^2 - x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y - x^57*z0 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^55*y + x^14*z0,
 x^114 - x^112*z0^2 + x^112*z0 + x^111*z0^2 - x^112 - x^111*y - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^102*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*z0 + x^96*y*z0 + x^96*z0 - x^94*y*z0^2 + x^95*y + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^93 + x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*z0 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y - x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^84*y + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*z0 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 - x^80*y - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*z0 - x^71 + x^70*y + x^69*z0^2 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^55*y*z0 - x^56 - x^55*y + x^14*z0^2,
 -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^109*y*z0 - x^109*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^107*z0^2 + x^106*y*z0^2 + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*y + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^92*z0^2 + x^93 - x^92*y + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*z0 + x^89*z0^2 - x^89*y - x^89*z0 + x^88*z0^2 + x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^87*y - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*y - x^86*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*z0^2 - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^77*y*z0 - x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*z0 + x^75*y - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 - x^69*y*z0^2 + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*y + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^62*z0^2 - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^55*y*z0 - x^56 + x^55*y + x^14*y,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*z0^2 - x^111 + x^110*z0 + x^108*y*z0^2 - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^107*y - x^106*z0^2 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*y*z0 - x^104 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*y + x^99*z0 + x^98*z0^2 - x^99 + x^98*y - x^98*z0 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 - x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^93 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 - x^73*z0 - x^72*y*z0 + x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^72 + x^70*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*z0 - x^60*z0^2 - x^61 - x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^14*y*z0,
 x^115 + x^114*z0 - x^114 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 + x^111*y + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^103*y*z0^2 + x^105 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*y + x^98*z0^2 - x^99 - x^98*y - x^98*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 - x^97 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^93*y*z0 - x^93*z0^2 + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^91 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^87*y*z0 + x^88 + x^87*y - x^86*y*z0 + x^85*y*z0^2 - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 + x^80*y*z0^2 - x^81*y + x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^80*z0 - x^79*z0^2 - x^80 + x^79*y + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^73*y*z0 + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*z0 - x^70*z0^2 + x^71 + x^70*y + x^69*y*z0 - x^69*z0^2 + x^69*z0 + x^68*y*z0 + x^69 + x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 - x^63*y*z0^2 + x^64*y + x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*y*z0 - x^62 + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^58*y*z0^2 + x^60 - x^58*y*z0 - x^58*y + x^58 + x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^55*y*z0 + x^56 - x^55*y + x^14*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*y + x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y + x^106*z0 + x^105*z0^2 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*z0 - x^103*y*z0 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*z0 - x^101*y*z0 - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*y + x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^86*y*z0 + x^85*y*z0^2 - x^87 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*z0 - x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^82*z0 + x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 + x^81 - x^79*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*z0 - x^77*z0^2 - x^77*y + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^74*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*y - x^66*z0^2 - x^66*y - x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^64*z0 + x^62*y*z0^2 - x^64 - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y + x^58*z0 - x^58 - x^56*y + x^56*z0 + x^56 - x^55*y + x^15,
 x^115 + x^114*z0 + x^114 + x^113*z0 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^108*y*z0 - x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^107*z0 - x^106*y*z0 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^99*y*z0 + x^98*y*z0^2 + x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^93*y*z0^2 - x^95 + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*z0^2 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*z0^2 + x^79 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y + x^74*y*z0 - x^74*z0^2 - x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^70*y*z0 + x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 + x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*z0 + x^60*y*z0 - x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0 + x^56 + x^15*z0,
 x^115 + x^114*z0 - x^114 + x^113*z0 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 - x^110*y + x^110*z0 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 - x^106*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y - x^102*z0^2 + x^103 - x^102*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 + x^95 - x^94*z0 + x^93*y*z0 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 + x^88*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^84 + x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*z0^2 - x^77 - x^76*y - x^75*z0^2 + x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^73*y + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^71*y + x^70*z0^2 - x^71 + x^70*y + x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^66*y*z0^2 - x^67*z0 + x^67 + x^66*y - x^66*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^61 + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y - x^56*z0 - x^56 + x^15*z0^2,
 -x^115 - x^114*z0 - x^114 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*z0^2 + x^111 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^108*y*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 - x^106 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y + x^103*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^102*z0 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^97*y*z0 - x^97*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^94*y*z0 + x^95 + x^94*z0 + x^93*y*z0 - x^94 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*y + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0 + x^84*z0^2 - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^81*y*z0 - x^80*y*z0^2 + x^82 + x^80*y*z0 + x^79*y*z0^2 - x^80*y + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^74*y*z0^2 - x^76 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 + x^71*z0^2 - x^71*y + x^71*z0 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 + x^65*y*z0^2 + x^66*y + x^66*z0 - x^65*y*z0 - x^66 - x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^56 + x^15*y,
 -x^115 + x^113*z0^2 + x^114 - x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^108*y*z0 + x^108*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^105*y - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^101*y*z0^2 + x^103 + x^101*y*z0 - x^102 + x^101*y - x^101*z0 + x^100*z0^2 + x^101 - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^92*y*z0 - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^86*y*z0 - x^85*y*z0^2 + x^87 - x^86*y + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*y + x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^74 + x^73*y - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72 + x^71*y + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^69*y*z0 - x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 + x^67 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y - x^58*y*z0 - x^59 - x^58*y + x^58*z0 + x^56*y*z0^2 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^15*y*z0,
 x^115 + x^114*z0 - x^114 - x^112*z0^2 - x^113 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*y + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^109*y*z0 - x^109*z0^2 + x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^101 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^97*y*z0^2 - x^99 + x^98*y + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*z0 + x^94*y*z0 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^79*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^73*y - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^65*y*z0^2 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^64*y*z0 + x^64*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^59*y - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^15*y*z0^2,
 x^114*z0 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^110 - x^109*y + x^109*z0 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^105 + x^104*y + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*z0^2 - x^102*y + x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^99*y - x^99*z0 + x^98*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^97*y + x^96*y*z0 - x^96*z0^2 - x^97 + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*y - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^89*y*z0 - x^90 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^78*z0^2 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^77*y + x^76*y*z0 - x^76*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^71*y*z0^2 - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y + x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*z0^2 + x^58 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^16,
 -x^115 + x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*z0 + x^108*y*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 - x^106 - x^105*z0 - x^104*y - x^104*z0 - x^103*z0^2 + x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^100*y*z0 + x^100*z0^2 - x^101 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^96 + x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*y + x^93*z0 - x^93 - x^92*z0 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^88 + x^87*z0 + x^87 + x^86*z0 + x^85*z0^2 - x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 - x^83*z0^2 + x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^80*z0^2 + x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^74*y*z0 + x^74*z0^2 - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*z0 + x^71*y*z0^2 - x^73 - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^58*y*z0 + x^57*y*z0^2 + x^58*y + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^16*z0,
 -x^114*z0 - x^113*z0^2 - x^114 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^108*z0 - x^106*y*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0 - x^103*y*z0 - x^103*y + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^98 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^94*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^86*y*z0 - x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 + x^84*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y + x^77*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^70*y - x^69*y*z0 - x^68*y*z0^2 + x^70 - x^68*y*z0 + x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*z0 - x^59*z0^2 - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^16*z0^2,
 x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 + x^113 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y - x^110*y*z0 + x^110*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^105*y*z0^2 + x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^98 + x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^93*y*z0^2 + x^95 + x^94*y + x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y - x^88*z0 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^82*z0^2 - x^81*y*z0 + x^81*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*z0 + x^79*z0^2 - x^79*y + x^78*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^73*y - x^72*y*z0 - x^72*z0^2 + x^73 - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y - x^70*y*z0 - x^70*y + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 + x^66*z0 + x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y + x^16*y,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^111 + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^106*y - x^104*y*z0^2 + x^106 + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 + x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^100*z0^2 - x^100*y - x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 - x^98 + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*y + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^92*z0 - x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^85*y*z0^2 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^83*y + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^81 + x^79*z0^2 - x^80 - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y - x^77*z0^2 - x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^75*z0^2 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 + x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^71 + x^70*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 - x^65*y*z0^2 - x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^62*z0^2 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^58 - x^57*z0 + x^56*z0^2 + x^56*z0 + x^56 + x^55*y + x^16*y*z0,
 -x^115 - x^114*z0 - x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^111*y + x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^104*y - x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 + x^97 - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*z0^2 - x^93*z0 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 + x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^83 - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 + x^72*z0 - x^72 + x^71*y - x^71*z0 - x^69*y*z0^2 - x^70*z0 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^66 + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^59*y*z0^2 - x^60*y - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^56*z0 - x^55*y + x^16*y*z0^2,
 x^115 - x^113*z0^2 + x^114 + x^112*z0^2 + x^113 - x^112*y + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*z0^2 - x^106*y - x^106*z0 - x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*z0 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^97*z0 - x^96*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^96 - x^94*y*z0 - x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^94 - x^93*z0 - x^91*y*z0^2 - x^91*y*z0 + x^91*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^79*y - x^79*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^72*y*z0 - x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y - x^66*z0^2 - x^67 - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^55*y*z0 - x^56 + x^55*y + x^17,
 x^115 + x^114*z0 + x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^112 - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*z0 + x^107*y*z0 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*z0^2 + x^104*y + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^103 - x^102*y + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^98*y*z0 + x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^98 + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 - x^82 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^80 + x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^76 - x^75*y - x^75*z0 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^71*y*z0 - x^71*z0^2 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^63 - x^61*y*z0 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56 + x^55*y + x^17*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*y + x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^109 - x^107*y*z0 + x^108 - x^107*z0 + x^106*y*z0 - x^107 + x^106*y - x^105*y*z0 + x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^99*z0^2 + x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^93*y*z0^2 + x^94*y - x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^91 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*z0 + x^87*z0^2 - x^87*y - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 + x^84*y - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^80*y*z0 + x^80*z0^2 + x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^77*y*z0^2 - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^69*y*z0^2 + x^70*y + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^67 + x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^64 + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^56*y*z0 + x^55*y*z0 + x^17*z0^2,
 x^115 - x^113*z0^2 + x^113 - x^112*y + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^110*z0^2 - x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 + x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*z0 + x^101*y*z0 + x^101*z0 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*z0 + x^97*y*z0^2 - x^98*y + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*z0 - x^95*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90*y*z0 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 + x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^87*y - x^86*y*z0 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^66*y*z0^2 - x^68 + x^67*y + x^66*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*z0^2 + x^62*y + x^62*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 + x^59 + x^58*y - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^56*y - x^55*y*z0 - x^56 + x^55*y + x^17*y,
 x^114*z0 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^109*y + x^108*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^105 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^100*y*z0^2 + x^101 - x^100*z0 - x^98*y*z0^2 + x^100 - x^99*y + x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^90*y*z0^2 - x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 - x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*z0^2 + x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*z0^2 - x^82 + x^81*y + x^80*y*z0 + x^79*y*z0 - x^79*z0^2 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*z0 + x^69*y*z0 - x^68*y*z0^2 + x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 - x^68 + x^66*z0^2 - x^67 + x^66*y - x^64*y*z0^2 + x^66 - x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^61*y*z0^2 - x^63 + x^61*z0^2 + x^62 - x^61*z0 - x^60*z0^2 + x^60*y - x^60*z0 + x^58*y*z0^2 - x^60 + x^58*z0^2 - x^59 - x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^17*y*z0,
 -x^115 - x^114*z0 - x^114 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^112 + x^111*y - x^111*z0 + x^110*z0^2 - x^110*y + x^109*y*z0 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108 - x^107*y - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^102*y*z0^2 - x^104 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^99 + x^98*z0 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*y + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^85*y*z0 - x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*z0 - x^83*y*z0 - x^84 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*y + x^74*y*z0 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^70*y*z0^2 - x^71*y - x^71*z0 - x^69*y*z0^2 - x^71 + x^70*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^67*y*z0^2 + x^69 + x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*z0 + x^66*y + x^66*z0 - x^65*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^55*y*z0 + x^56 - x^55*y + x^17*y*z0^2,
 x^115 + x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^110*y - x^109*z0^2 + x^108*y*z0^2 + x^109*y - x^109*z0 + x^108*y*z0 + x^109 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^107 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*z0^2 + x^99*y + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^98 + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*y + x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^91*z0 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^86 + x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^83*y*z0 - x^82*y*z0^2 - x^84 + x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 + x^81*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^77*y*z0^2 - x^78*y + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 + x^66*y*z0^2 - x^67*y + x^66*z0^2 + x^67 - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^62 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^18,
 -x^114*z0 - x^113*z0^2 - x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 + x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^106 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^100 + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^97*y*z0 - x^96*y*z0^2 - x^97*y - x^96*y*z0 - x^96*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^87 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^84*y*z0 - x^85 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*y + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 - x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^68*y + x^68*z0 - x^66*y*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^61 + x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*z0 + x^56*y*z0 - x^56*y - x^55*y + x^18*z0,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*y + x^109*z0 - x^108*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 - x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^97*y - x^96*y*z0 - x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^91*z0^2 - x^90*y*z0^2 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y + x^88*z0^2 - x^89 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^65*z0^2 + x^64*y*z0^2 + x^66 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^63*y - x^63*z0 + x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^59*z0^2 - x^60 - x^59*y + x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*z0^2 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^18*z0^2,
 x^114*z0 + x^113*z0^2 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*z0 - x^111 + x^109*z0^2 - x^110 + x^109*y + x^108*y*z0 + x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 - x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^94*y + x^93*y*z0 + x^94 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 - x^91 + x^90*y - x^89*z0^2 + x^90 + x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*z0^2 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 + x^81*y + x^80*z0^2 - x^81 + x^80*y - x^80*z0 - x^80 - x^79*y - x^78*z0^2 + x^79 + x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*z0 - x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^65*y*z0 + x^65*z0^2 + x^65*z0 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0 - x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y*z0 + x^55*y*z0 - x^56 + x^55*y + x^18*y,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^110 - x^109*y + x^108*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 - x^107 - x^106*y - x^106*z0 + x^105*z0^2 + x^105*y + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^102*y*z0 - x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 - x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 - x^93 - x^92*y - x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 - x^88*y*z0 + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^85*y*z0 + x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*y + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*z0 - x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*y + x^76*y*z0 + x^76*z0^2 - x^76*y - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 + x^70*y*z0^2 + x^72 + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^68 + x^67*y - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^18*y*z0,
 -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*z0 + x^105*y*z0 + x^104*y*z0^2 + x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^102 + x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*z0 + x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^93*y*z0 - x^93*z0^2 - x^94 + x^93*y - x^93*z0 + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*y + x^84*y*z0 + x^85 - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^84 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 + x^81 + x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^77*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^71*y + x^70*y*z0 - x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 + x^67 - x^66*y + x^66*z0 - x^65*z0^2 - x^66 + x^65*y - x^65*z0 + x^63*y*z0^2 - x^64*y - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^61 + x^60*y - x^60*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 - x^58*z0^2 + x^57*y*z0^2 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^55*y*z0 + x^56 + x^18*y*z0^2,
 -x^115 - x^114*z0 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*z0 - x^105*y*z0 - x^106 + x^105*y - x^105*z0 - x^104*z0^2 - x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*z0 + x^99*z0^2 + x^100 - x^99*y + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y - x^97*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*z0 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^90 - x^89*y - x^89*z0 + x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^84*y + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*y*z0 + x^82*y + x^81*y*z0 + x^81*z0^2 + x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 + x^76*z0^2 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^74*z0 - x^73*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*y*z0 - x^72 + x^70*y*z0 + x^70*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y + x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 - x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^55*y*z0 + x^55*y + x^19,
 x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 + x^110*z0 - x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^102 - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^99*z0^2 + x^98*y*z0^2 - x^98*z0^2 - x^97*y*z0^2 - x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*y - x^96*z0 - x^95*z0^2 + x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*y + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*y*z0 + x^84 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 - x^76 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^71*y + x^70*y*z0 + x^70*z0^2 + x^71 - x^70*y - x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^68 + x^67*y + x^65*y*z0^2 - x^66*z0 - x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 - x^64*z0 + x^63*y*z0 + x^62*y*z0^2 + x^64 - x^63*y + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*z0^2 - x^60 + x^59*y + x^57*y*z0^2 - x^59 + x^58*y + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^57 - x^56*y + x^56*z0 + x^56 + x^19*z0,
 x^114 + x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^109*y*z0 + x^108*y*z0^2 + x^110 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*z0^2 - x^108 - x^107*y + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 + x^104 - x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^102 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y + x^97*y*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^92*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^90 + x^89*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^86*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^77*y*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^77 - x^76*y - x^75*y*z0 - x^74*y*z0^2 + x^76 - x^75*y + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 - x^71*y - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 - x^66*y*z0^2 + x^67*z0 + x^66*z0^2 + x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^63*y*z0^2 - x^64*y - x^63*y*z0 + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^62 + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*z0 - x^55*y*z0 + x^19*z0^2,
 -x^115 + x^113*z0^2 - x^114 + x^113*z0 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^111 - x^110*y + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^109 + x^108*y - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^105*y + x^105*z0 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 + x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 + x^99*y*z0 + x^100 + x^99*z0 - x^98*y*z0 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 + x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^89*z0 + x^88*z0^2 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*z0^2 + x^83 - x^82*y - x^81*y*z0 - x^81*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*z0 - x^76*y*z0^2 - x^77*z0 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 + x^72*y + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^70*y + x^70*z0 - x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^69 - x^68*y + x^68*z0 + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*z0^2 + x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y - x^62*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^61 + x^59*y*z0 + x^58*y*z0^2 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^19*y,
 x^114*z0 + x^113*z0^2 + x^113*z0 - x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 + x^111 + x^110*y - x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^109 - x^108*y + x^108*z0 - x^108 + x^107*y - x^107*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^100 - x^99*y + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^92*y*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*z0 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^77*y*z0^2 + x^78*y + x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^77 - x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^71*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^70 + x^69*y + x^68*y*z0 + x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^65*z0^2 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 + x^56 - x^55*y + x^19*y*z0,
 x^115 - x^113*z0^2 + x^114 - x^113 - x^112*y - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*z0^2 + x^110*y + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 + x^107*y*z0^2 - x^109 + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^101*z0^2 + x^100*y*z0^2 + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^90*y - x^89*y*z0 - x^89*z0^2 - x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 + x^87*y*z0 + x^86*y*z0^2 + x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y + x^83*y*z0 + x^84 - x^83*z0 - x^82*y*z0 - x^83 - x^82*y - x^82*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^79 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^76*y*z0 + x^77 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*z0^2 - x^74 - x^73*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^69 - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 - x^56*y*z0^2 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*z0 + x^56 + x^55*y + x^19*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^107*z0 + x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*z0 - x^103*z0^2 + x^104 - x^103*y + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 - x^103 + x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^98 - x^97*y - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*z0^2 - x^96 + x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^86*y*z0 + x^86*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y - x^84*y*z0 - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 - x^83 - x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^74*y - x^73*z0^2 + x^74 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 + x^66*y*z0^2 - x^68 + x^67*y - x^65*y*z0^2 + x^67 + x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*z0 - x^62*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^20,
 x^115 + x^114*z0 - x^114 + x^113*z0 - x^113 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^111*y - x^110*y*z0 + x^110*z0^2 + x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 + x^103*y*z0^2 - x^105 + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*z0 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^100 - x^99*y - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 + x^96 + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y - x^85*y*z0 - x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^82*z0^2 - x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 - x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*z0^2 - x^73 - x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^71*y + x^71*z0 - x^69*y*z0^2 + x^71 + x^70*y + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^67 - x^65*y*z0 - x^66 + x^65*z0 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 + x^60*y*z0^2 - x^62 + x^61*z0 + x^59*y*z0^2 + x^60*z0 + x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^58 - x^57*y - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^20*z0,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 + x^109*y - x^109*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*z0^2 - x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^99*y*z0 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^91 + x^89*z0^2 - x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^84 - x^83*y + x^82*y*z0 + x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^80*y*z0 + x^79*y*z0^2 - x^81 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*y - x^77*z0^2 + x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y + x^70 + x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^66*z0 + x^65*z0^2 - x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 + x^58*y*z0^2 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*y + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^55*y*z0 + x^20*z0^2,
 -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^113 + x^112*y - x^110*y*z0^2 - x^112 - x^111*y - x^109*y*z0^2 - x^111 - x^110*y + x^109*z0^2 + x^110 + x^109*y - x^109*z0 - x^108*z0^2 + x^108*y - x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^106*y*z0 - x^106*z0^2 + x^107 - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^105*y - x^105*z0 + x^104*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 + x^100*y*z0^2 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 + x^99*z0^2 - x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 - x^95*z0 - x^94*z0^2 - x^94*y - x^93*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^92*y - x^92*z0 + x^91*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^87*y*z0 - x^87*z0^2 - x^88 + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^84 - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0 - x^78*z0^2 + x^77*z0^2 - x^76*y*z0^2 - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^76*z0 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 - x^75 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y - x^61*z0 - x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y + x^20*y,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*y - x^104*z0 - x^103*y*z0 - x^104 + x^103*y - x^102*z0^2 - x^102*y - x^101*z0^2 - x^100*y*z0^2 - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*z0 + x^95*z0^2 + x^95*z0 - x^94*z0^2 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*z0 + x^89 + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*y*z0 + x^87 + x^86*y + x^85*y*z0 + x^85*y - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^79*y*z0 + x^79*z0^2 - x^80 - x^79*z0 + x^78*y*z0 + x^79 + x^78*y + x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^70*y*z0 + x^69*y*z0^2 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^69*z0 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^65 + x^64*y + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 - x^57*z0^2 - x^58 + x^57*y + x^56*y*z0 - x^56*z0^2 + x^56*z0 - x^55*y*z0 + x^20*y*z0,
 -x^115 + x^113*z0^2 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 - x^110*y*z0^2 - x^112 - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^106*y - x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*z0^2 + x^101 - x^100*z0 - x^98*y*z0^2 + x^100 + x^98*y*z0 + x^99 - x^98*y - x^98*z0 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^94*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^94 - x^92*y*z0 - x^92*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 - x^88*y - x^88*z0 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*z0 - x^81*z0^2 - x^82 - x^81*y + x^80*z0^2 + x^79*y*z0^2 + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^76*y*z0^2 - x^77*z0 + x^76*y*z0 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^75 - x^73*y*z0 - x^73*z0^2 + x^73*y + x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 + x^69*z0^2 - x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*z0 - x^67*z0^2 + x^68 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 + x^60*y*z0^2 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 - x^57*z0^2 - x^57*z0 + x^56*y*z0 + x^57 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^20*y*z0^2,
 -x^115 + x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^102*y*z0^2 + x^104 - x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*z0 - x^98*y*z0 + x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*z0^2 - x^93 + x^92*z0 + x^91*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*y + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^87 - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^85 - x^84*y - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0 + x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^77*z0 + x^76*z0^2 + x^77 + x^76*y - x^75*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*z0^2 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 + x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y - x^60*z0 + x^59*y*z0 + x^60 - x^59*z0 - x^58*z0^2 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^21,
 x^115 + x^114*z0 - x^113*z0 - x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^106*y*z0 + x^106*y - x^105*y*z0 + x^105*y + x^104*y*z0 + x^104*z0^2 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^104 - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 + x^101 + x^100*z0 - x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 - x^85*z0^2 - x^85*y - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 - x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^81*z0 - x^80*y*z0 + x^79*y*z0^2 + x^81 - x^80*y - x^79*y*z0 + x^79*y + x^79*z0 - x^78*y*z0 + x^79 - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0 - x^72*y*z0^2 - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 + x^70*y + x^69*z0^2 + x^69*y + x^69*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^66*z0^2 + x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^21*z0,
 -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 + x^105*z0^2 - x^104*y*z0^2 - x^104*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 - x^100*y + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y + x^98*z0^2 + x^99 + x^98*z0 + x^96*y*z0^2 + x^97*y - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*z0 - x^92*y*z0 - x^93 + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y - x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^86*y + x^85*z0^2 + x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y - x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 + x^69 - x^68*y + x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^61*y + x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*y + x^59*y*z0 + x^58*y*z0 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^56*y*z0^2 - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y - x^55*y*z0 + x^56 + x^21*z0^2,
 x^115 - x^113*z0^2 - x^114 - x^113 - x^112*y - x^112*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*z0^2 - x^111 + x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100 + x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y + x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^97 - x^96*z0 + x^95*y*z0 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^92*z0 - x^90*y*z0^2 + x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^85*y*z0 + x^84*y*z0^2 + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^80*y*z0^2 + x^82 + x^81*y + x^80*y*z0 - x^80*y - x^79*z0^2 + x^80 + x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^76 - x^75*z0 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 + x^72*y*z0 - x^72*z0^2 - x^73 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^71*y - x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^68*y*z0^2 - x^70 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^65 - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^63*y + x^62*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60 + x^59*y - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^58 - x^57*y + x^56*z0^2 + x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^21*y,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 + x^105*y*z0^2 - x^107 - x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 - x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*z0^2 + x^83*y + x^82*y*z0 + x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^82 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^79*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 + x^76*z0^2 - x^77 + x^76*z0 + x^75*y*z0 + x^76 + x^75*y - x^75 + x^74*y + x^74*z0 - x^73*z0^2 + x^74 - x^73*y - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^70*y + x^69*y*z0 - x^69*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*z0^2 + x^68 + x^67*z0 - x^67 + x^66*z0 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^63*y - x^62*y*z0 + x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*z0^2 + x^61 + x^60*z0 - x^58*y*z0^2 + x^60 - x^59*y - x^58*z0^2 - x^57*y*z0^2 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^21*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^108*z0^2 - x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y - x^102*z0 + x^101*z0^2 + x^102 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*z0 - x^97*y*z0^2 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 - x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0 - x^87*y*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*z0 - x^86*y*z0 - x^87 - x^86*y + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^85*y - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^76*y*z0 - x^76*z0^2 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^74*y + x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^74 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^70*z0 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^66*z0^2 + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*z0^2 + x^61 + x^60*y - x^59*y*z0 + x^58*y*z0^2 - x^59*y + x^58*z0^2 + x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^21*y*z0^2,
 -x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^110*z0 - x^109*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 + x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^102 - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*z0 + x^99*z0^2 + x^100 + x^99*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*y - x^95*y*z0 - x^95*z0^2 - x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^94 - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y + x^92*z0 - x^90*y*z0^2 + x^91*z0 - x^90*y*z0 - x^91 + x^90*y - x^90*z0 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 - x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^85*y - x^84*z0^2 + x^85 - x^84*y - x^83*y*z0 - x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y + x^82 + x^81*y - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^76*y*z0 - x^75*y*z0^2 - x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*y + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^65*y*z0^2 + x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y - x^63*z0^2 + x^64 + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^22,
 x^114*z0 + x^113*z0^2 - x^113*z0 + x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 + x^111 - x^110*y - x^109*y*z0 + x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*z0^2 + x^108 - x^107*y - x^107*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^106 + x^105*y + x^104*y*z0 + x^104*z0^2 - x^105 - x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*z0^2 + x^100 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^94*y*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y + x^88*z0^2 - x^89 - x^88*z0 + x^86*y*z0^2 - x^87*y + x^86*y*z0 - x^87 + x^86*y - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*z0^2 - x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^72*y*z0 - x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 + x^62*y*z0^2 + x^64 - x^62*y*z0 - x^61*y*z0^2 + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*z0^2 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^58*y + x^58*z0 - x^56*y*z0^2 + x^58 - x^57*y - x^56*y*z0 - x^56*z0^2 - x^56*z0 - x^55*y + x^22*z0,
 x^114 + x^112*z0^2 + x^113 - x^111*z0^2 - x^111*y - x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 + x^110 - x^109*z0 + x^108*z0^2 - x^109 + x^108*y + x^107*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y - x^103*y*z0 + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y + x^93*y*z0 - x^93*z0^2 - x^94 - x^92*y*z0 - x^91*y*z0^2 - x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^92 + x^91*y + x^91*z0 - x^89*y*z0^2 + x^90*y + x^89*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^87*z0 - x^86*y*z0 - x^86*z0 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^71*z0^2 - x^72 - x^71*y + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*z0^2 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*z0 + x^66*z0^2 - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^66 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^64*y - x^64 - x^63*y - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 - x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y + x^56*y*z0 + x^56*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^22*z0^2,
 -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*y + x^107*z0^2 + x^106*y*z0^2 - x^107*z0 + x^106*z0^2 - x^106*y + x^106*z0 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y - x^100*z0 - x^99*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y - x^95*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^89 + x^88*y - x^88*z0 + x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^83 - x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^76 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*z0^2 + x^71 - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^69*z0 - x^68*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^64 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 - x^61*y*z0 - x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^56*y - x^56*z0 + x^55*y*z0 + x^22*y,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y - x^110*z0 + x^110 + x^108*y*z0 + x^107*y*z0^2 + x^109 + x^108*y + x^107*y*z0 + x^107*z0^2 - x^108 + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*y*z0 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^102 - x^100*y*z0 - x^100*z0 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^83*y*z0^2 - x^85 - x^84*z0 + x^83*y*z0 - x^82*y*z0^2 + x^84 + x^83*y + x^83*z0 - x^83 - x^82*y + x^81*z0^2 + x^82 + x^79*z0^2 + x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^76*z0 + x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 + x^74*y - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*z0 - x^71*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^67*y + x^65*y*z0^2 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^60 - x^59*y - x^59 - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^22*y*z0,
 -x^115 + x^113*z0^2 + x^112*z0^2 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*z0 + x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 + x^107*y*z0 + x^107*y - x^107*z0 - x^106*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*z0 - x^104 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^100 - x^99*z0 + x^98*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*z0 + x^90*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*z0^2 + x^88*z0 - x^87*y*z0 + x^86*y*z0^2 + x^88 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 - x^83*z0^2 - x^82*y*z0^2 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 + x^80*y*z0^2 + x^82 + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^76*y - x^75*y*z0 - x^74*y*z0^2 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^73*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^68*z0^2 + x^67*y*z0^2 + x^68*y - x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 + x^67 - x^66*y + x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y - x^56*z0 + x^22*y*z0^2,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^103*y*z0^2 + x^105 + x^104*z0 + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 - x^100*y + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^94 + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*z0 + x^89*y*z0 + x^90 + x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^88*y + x^87*y*z0 + x^86*y*z0^2 + x^88 - x^86*z0^2 - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^83*y + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y - x^79*y*z0 - x^78*y*z0^2 - x^78*z0^2 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 + x^61*z0 - x^59*y*z0^2 + x^61 - x^60*z0 + x^59*z0^2 - x^60 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*z0 - x^56 + x^55*y + x^23,
 -x^115 + x^114*z0 - x^113*z0^2 + x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^111*z0 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 + x^108*y*z0 - x^108*y + x^108*z0 - x^107*y*z0 - x^106*y*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^104*y*z0^2 - x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*z0 - x^103*z0^2 - x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*y + x^98*z0^2 - x^98*z0 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y - x^90*y*z0^2 + x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 - x^87*y*z0 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^83 - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^76*y*z0^2 + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^72*z0 - x^71*y*z0 - x^72 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^67 - x^66*z0 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^63*z0^2 + x^62*y*z0^2 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^58*y*z0^2 + x^60 - x^59*y - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y - x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^56*z0^2 + x^57 + x^56 - x^55*y + x^23*z0,
 -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^105*y + x^105*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^102 + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y - x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^98*z0 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^94*y*z0 - x^93*y*z0^2 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^92*z0^2 + x^93 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y*z0 + x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^87*y*z0 - x^87*z0^2 - x^87*y - x^87*z0 - x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*z0^2 + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*y + x^79*z0^2 - x^79 - x^78*y - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*z0 - x^75*y*z0 - x^76 + x^75*y - x^75*z0 + x^73*y*z0^2 - x^74*y - x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y - x^73*z0 - x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y + x^68*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^63 + x^62*y - x^61*y*z0 + x^62 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*z0 - x^58*y*z0^2 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y + x^57*y*z0 - x^58 + x^57*z0 + x^56*y*z0 - x^57 - x^56*y + x^55*y*z0 - x^55*y + x^23*z0^2,
 x^114*z0 + x^113*z0^2 + x^114 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^103 - x^102*y - x^101*y*z0 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*z0 - x^98*y*z0^2 - x^100 - x^99*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y - x^97*y*z0 + x^96*y*z0^2 - x^97*y + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*z0^2 + x^96 - x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^93*y*z0 - x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 + x^92*y - x^91*y*z0 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 + x^89 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y - x^83*z0 - x^82*z0^2 - x^83 - x^82*y - x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^75*y - x^75*z0 - x^73*y*z0^2 + x^75 - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 - x^65*y*z0^2 + x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0 + x^56*z0^2 - x^57 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^23*y,
 -x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^106*z0 + x^105*y*z0 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*z0^2 - x^98*y + x^98*z0 - x^97*z0^2 - x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 + x^91*z0^2 - x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^87*y*z0^2 - x^89 + x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^86*z0 - x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^78*y - x^77*y*z0 + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*y - x^76 - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^71*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^69*z0^2 + x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*y + x^65*y*z0^2 + x^66*z0 + x^65*z0^2 + x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^61 - x^60*y + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^58 + x^57*z0 + x^56*z0^2 - x^57 + x^56*z0 + x^55*y*z0 + x^56 + x^23*y*z0,
 x^115 + x^114*z0 - x^114 - x^112*z0^2 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*z0 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*z0 - x^95*y*z0 + x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^94*z0 - x^93*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*z0 + x^84*y*z0 - x^84*y - x^84*z0 + x^84 - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*y - x^81*z0^2 + x^82 + x^81*z0 - x^80*y*z0 + x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^79*z0 + x^78*z0^2 - x^78*y - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y - x^73*y*z0 - x^73*z0^2 + x^74 + x^73*y - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^70*y - x^69*z0^2 - x^70 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^66 - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*z0^2 + x^57 + x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^23*y*z0^2,
 x^115 + x^114*z0 + x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^106*y*z0 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^100 - x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^94*y*z0^2 + x^96 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^93*z0 - x^92*y*z0 + x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 + x^90*y*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*y - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 + x^85 - x^84*y - x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 + x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 - x^71*z0^2 - x^72 + x^70*y*z0 + x^69*y*z0^2 + x^71 - x^70*y + x^69*y*z0 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*z0^2 + x^68 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^63*y - x^63*z0 + x^62*z0^2 + x^62*y + x^62*z0 - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*z0 - x^56 + x^24,
 -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^113 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^102*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*z0^2 + x^101 - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^97*y*z0 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^90*y*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y + x^87*z0^2 + x^88 + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*z0^2 - x^85 - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*z0^2 - x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^70*y - x^70*z0 + x^69*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^66*z0 + x^64*y*z0^2 + x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*y - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*y - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*z0 - x^58*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*z0^2 - x^57*y - x^57 - x^56*y + x^56*z0 + x^55*y*z0 - x^55*y + x^24*z0,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*z0^2 - x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^106*z0^2 + x^107 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*y + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^82 + x^81*y + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 + x^75*y - x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^73*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*z0^2 - x^71 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 + x^69*y + x^68*y*z0 - x^68*z0^2 - x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^65*y*z0 + x^65*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*z0^2 - x^64*y - x^63*z0^2 + x^63*y + x^63*z0 + x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^55*y + x^24*z0^2,
 x^113*z0 - x^112*z0 - x^111*z0^2 - x^110*y*z0 - x^110*z0^2 + x^111 - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^103*y - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^102*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^96 - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^93*z0 + x^92*y*z0 - x^93 + x^92*y - x^92*z0 - x^91*z0^2 - x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*z0^2 - x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^85 + x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^76*y + x^76*z0 - x^76 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^71*y*z0^2 + x^73 + x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 + x^66*y + x^65*y*z0 - x^65*z0^2 - x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*y*z0 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^24*y,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*z0^2 + x^109*y - x^109*z0 - x^108*y*z0 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^104*y*z0^2 + x^106 + x^105*z0 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 - x^93 - x^92*y - x^92*z0 + x^91*y*z0 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*z0 - x^86*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^85 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y + x^79*y*z0^2 - x^80*y + x^79*y*z0 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^76*y*z0 - x^76*z0^2 + x^76*y - x^76*z0 + x^74*y*z0^2 - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*z0 + x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*z0 - x^66 - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 + x^64 - x^63*y - x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*z0 + x^62 - x^61*z0 - x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^55*y*z0 - x^56 + x^24*y*z0,
 -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 + x^109*y - x^107*y*z0^2 + x^109 + x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*y*z0 + x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 - x^102*z0^2 - x^103 + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 - x^98*y - x^98*z0 - x^96*y*z0^2 - x^98 - x^97*y - x^96*z0^2 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^93 - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^88 - x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^86 + x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^83*y*z0 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 - x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 + x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^57*y + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^55*y*z0 + x^56 + x^24*y*z0^2,
 x^115 - x^113*z0^2 - x^113*z0 - x^112*y - x^112*z0 + x^110*y*z0^2 - x^112 + x^110*y*z0 - x^110*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^106*y*z0^2 - x^108 - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^101*y*z0 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 - x^95*y + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^91*y*z0 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^89*y*z0 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*y*z0 + x^83 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^79*y*z0 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 - x^72*y*z0^2 - x^73*y - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*z0 + x^72 - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 + x^68*y + x^67*y*z0 + x^67*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^64*y*z0^2 - x^66 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 + x^63*z0^2 - x^63*y + x^62*y*z0 + x^62*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^56*z0 - x^56 + x^25,
 x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*y + x^104*y*z0 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*y - x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^97*y*z0 + x^98 - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^95*y*z0 - x^96 + x^95*y - x^94*y*z0 - x^95 - x^94*y + x^93*y*z0 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 + x^93 + x^91*z0^2 - x^92 + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0 - x^83*z0^2 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^81*z0^2 - x^80*y*z0^2 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^75*y + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^72*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^72 + x^71*z0 - x^70*y*z0 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^68*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 + x^67*z0 - x^66*z0^2 + x^66*y + x^64*y*z0^2 - x^66 - x^65*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^62 + x^61*z0 + x^60*y*z0 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 + x^55*y + x^25*z0,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 - x^113 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 + x^110*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y + x^104*y*z0 + x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 + x^100*y*z0 + x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 - x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^95*y - x^93*y*z0^2 + x^95 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 + x^93 - x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*z0^2 + x^87 + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^78*z0^2 - x^79 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 + x^77 - x^76*y - x^76*z0 + x^75*z0^2 - x^76 + x^75*y - x^75*z0 + x^73*y*z0^2 - x^75 - x^74*y + x^73*y - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*z0 + x^66*z0^2 + x^67 + x^66*y + x^65*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0 + x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 + x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^25*z0^2,
 x^115 - x^113*z0^2 - x^114 - x^113*z0 - x^112*y - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^111 - x^110*z0 + x^108*y*z0^2 - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y + x^103*y*z0 + x^104 + x^103*y + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y - x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^78 - x^77*y + x^76*y*z0 + x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^60 + x^58*y*z0 + x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*z0 + x^56*z0^2 + x^56 - x^55*y + x^25*y,
 x^115 + x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^99*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 - x^95*y*z0^2 + x^96*y + x^95*y*z0 - x^96 + x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^89*y*z0^2 + x^91 + x^89*y*z0 + x^89*z0^2 + x^89*y + x^88*y*z0 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 + x^84 - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y + x^81*y*z0 + x^80*y*z0^2 + x^82 - x^80*z0^2 + x^81 + x^79*y*z0 - x^79*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^69*y - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^64 + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 + x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*z0 - x^59*y*z0^2 + x^59*y*z0 + x^58*y*z0^2 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^57*y*z0 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*y + x^25*y*z0,
 -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^99*y*z0 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^99 - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^93*y*z0^2 - x^95 - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^92*y + x^91*y*z0 + x^92 + x^91*y - x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y + x^82*y + x^82*z0 + x^81*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*y - x^79*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*z0 - x^73*y*z0 + x^74 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^67*y*z0 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 - x^67 - x^66*y + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*z0^2 - x^61 + x^60*y - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*y + x^56*z0 + x^55*y*z0 - x^55*y + x^25*y*z0^2,
 -x^113*z0 + x^113 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^111 - x^110*y + x^109*z0^2 + x^110 - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^104*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 - x^103 - x^102*y + x^101*z0^2 - x^100*y*z0^2 + x^101*y + x^101*z0 - x^100*y*z0 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y - x^94*y*z0 + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 + x^93 - x^92*y - x^92 + x^91*y - x^91*z0 + x^89*y*z0^2 + x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 - x^84*y*z0^2 + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^78*y*z0 + x^77*y*z0^2 - x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^62*y*z0 - x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*z0 + x^60*z0^2 - x^60*y + x^59*y*z0 + x^59*z0^2 + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 - x^57 - x^56*y - x^56*z0 - x^55*y + x^26,
 -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^107 - x^106*z0 + x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^103*y*z0 - x^103*z0^2 - x^104 + x^102*y*z0 + x^102*z0^2 - x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^94 - x^93*y - x^92*z0^2 + x^93 - x^92*y + x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*y + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^82*y - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*z0 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^79 + x^77*y*z0 + x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 + x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 - x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*z0 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 + x^65*z0 + x^63*y*z0^2 + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*y*z0 + x^61*y - x^61*z0 - x^60*z0^2 + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*z0 + x^26*z0,
 -x^115 - x^114*z0 + x^113*z0 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^108*y*z0 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^102*y + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 + x^99*y*z0 + x^100 - x^99*y - x^99*z0 - x^98*y*z0 - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^96*y*z0 - x^96*z0^2 - x^97 - x^96*y + x^96*z0 - x^94*y*z0^2 - x^96 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 - x^88 + x^87*y + x^87*z0 + x^87 - x^85*z0^2 - x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^78*y + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^76*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*y*z0 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^69*y + x^69*z0 - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^66*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^64*y + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^62 + x^61*y + x^60*y*z0 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 - x^60 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^58*z0 - x^57*y*z0 + x^56*y*z0^2 - x^57*z0 + x^56*y*z0 + x^57 + x^56*z0 + x^55*y*z0 - x^55*y + x^26*z0^2,
 -x^115 - x^114*z0 + x^114 + x^113*z0 - x^112*z0^2 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^105*y - x^104*z0^2 + x^105 - x^104*y - x^104*z0 + x^103*y*z0 + x^104 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^100*y - x^99*y*z0 + x^99*z0^2 - x^99*y - x^98*y*z0 + x^98*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^97 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^92 + x^91*y - x^91*z0 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y + x^73*y*z0 + x^73*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 - x^71*y + x^71*z0 - x^69*y*z0^2 - x^71 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 - x^66 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^59*y - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^58 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^55*y*z0 - x^56 - x^55*y + x^26*y,
 x^115 - x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 + x^108*z0 - x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 + x^100*y - x^100*z0 - x^99*y*z0 + x^100 + x^98*y*z0 + x^97*y*z0^2 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^94*y + x^93*y*z0 + x^92*y*z0^2 + x^93*y + x^93*z0 + x^91*y*z0^2 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 + x^91 - x^90*y - x^90*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*z0^2 - x^87*y - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^85 + x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 - x^79 + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0 - x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^71*z0 + x^69*y*z0^2 + x^71 + x^70*y - x^69*y*z0 + x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y + x^68 - x^67*y - x^67*z0 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^60*y*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^55*y + x^26*y*z0,
 -x^113*z0 + x^112*z0^2 - x^113 + x^112*z0 + x^112 + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^107*y*z0 + x^107*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y + x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^99*y*z0 + x^100 + x^99*y - x^99*z0 - x^98*z0^2 + x^99 + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^95*z0^2 - x^94*y*z0^2 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^90*y + x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 - x^84*y*z0^2 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^71*z0 + x^70*z0^2 + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*y + x^67*z0^2 + x^67*y + x^67*z0 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^64*z0^2 - x^64*y - x^63*z0^2 + x^62*y*z0^2 - x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 + x^60 + x^59*y + x^58*z0^2 - x^57*z0^2 + x^58 - x^57*y + x^56*z0^2 - x^56*z0 - x^55*y*z0 - x^55*y + x^26*y*z0^2,
 -x^114 - x^112*z0^2 - x^112*z0 + x^111*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 + x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 + x^95*y - x^94*y*z0 + x^94*y + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^92 + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^78 - x^77*y - x^76*y*z0 + x^77 + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y + x^71*z0 + x^69*y*z0^2 + x^71 + x^69*z0^2 - x^68*y*z0^2 + x^69*y - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^65*y*z0 - x^65*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^59*z0 + x^58*y*z0 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 + x^56 + x^27,
 -x^115 + x^113*z0^2 + x^114 - x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^108*y*z0 - x^107*y*z0^2 + x^108*y + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*z0 - x^105*y*z0^2 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 - x^101*y*z0 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^100*y - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^93 - x^92*y - x^92*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^90*z0^2 - x^91 + x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 + x^85*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^83*y*z0 - x^83*z0^2 - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^75*y*z0^2 + x^77 - x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y + x^71*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 - x^63*z0^2 + x^64 - x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*z0 + x^61*y*z0 - x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^58 - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56 + x^27*z0,
 x^114*z0 + x^113*z0^2 + x^114 + x^112*z0^2 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^108 - x^107*y - x^106*y*z0 - x^105*y*z0^2 + x^107 + x^106*y + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^96*y*z0 + x^96*z0^2 + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^93*y*z0^2 - x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*z0^2 - x^87 - x^86*y + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 + x^83*y*z0^2 + x^85 - x^84*y + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^81*z0^2 - x^82 - x^81*y - x^80*y*z0 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 - x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0 + x^69 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^61*y + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*y + x^58*y*z0 + x^58*z0^2 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^27*z0^2,
 x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^113 - x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^111 + x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y + x^105*y*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^103*y*z0^2 + x^105 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^102 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 + x^99*z0^2 - x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^95*y*z0^2 - x^96*y - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*y - x^91*y*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^83*y*z0^2 + x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*z0 + x^79*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^78*z0 - x^77*y*z0 + x^78 - x^77*y + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*z0^2 + x^75*y + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^71 + x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^68 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^64*y*z0 - x^64*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^60 - x^59*y - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^56*y*z0 - x^56*z0^2 - x^56*y + x^56*z0 + x^55*y + x^27*y,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 + x^111*y*z0 - x^110*y*z0^2 + x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^110 + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y - x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*z0 - x^99*z0^2 - x^99*y + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^91*y*z0 - x^91*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 + x^90*z0 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^87*y*z0 + x^88 + x^87*y - x^86*z0^2 + x^87 + x^86*y + x^86 - x^84*y*z0 + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 + x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^66*y*z0^2 - x^68 - x^67*y - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^63*y*z0 + x^62*y*z0^2 + x^64 - x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 - x^59*y*z0^2 + x^61 - x^60*z0 - x^58*y*z0^2 - x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*y - x^55*y*z0 - x^56 + x^55*y + x^27*y*z0,
 -x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y - x^106*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 - x^103 + x^101*z0^2 + x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 + x^100*y + x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*z0^2 - x^98 - x^97*z0 + x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^89*z0^2 + x^88*y*z0^2 - x^88*y*z0 - x^88*z0 - x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^84 - x^82*y*z0 + x^82*z0^2 - x^82*y - x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y + x^76*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67 + x^66*y - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 + x^59 + x^58*y + x^58 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^27*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^108 - x^107*y - x^106*z0^2 + x^107 + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*y + x^104*z0 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^100*z0 + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*y*z0 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^93*y - x^93*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^90*y*z0^2 + x^92 - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 + x^90 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y - x^87*y*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^82*y*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^81*y*z0 + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*z0^2 - x^72 - x^71*y + x^70*y*z0 + x^70*z0^2 - x^71 + x^70*y - x^69*y*z0 - x^69*z0^2 + x^70 - x^69*y + x^69 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^66*y + x^66*z0 - x^64*y*z0^2 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^63 - x^62*y - x^61*y*z0 + x^61*z0^2 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56 + x^28,
 x^115 + x^114*z0 + x^114 - x^113*z0 + x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*z0^2 + x^110 + x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 + x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*z0 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 - x^96*z0^2 - x^96*y + x^96*z0 + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^90*z0^2 + x^89*y*z0^2 + x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^87 - x^86*y - x^86*z0 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^83*y*z0^2 - x^84*y - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^70 + x^69*z0 + x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*z0^2 - x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 - x^64 - x^63*z0 - x^62*y*z0 - x^63 + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*z0 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^56 + x^28*z0,
 x^115 + x^114*z0 + x^114 + x^113*z0 - x^113 - x^112*y - x^111*y*z0 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y + x^110*z0 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 + x^107*y*z0^2 - x^108*y - x^107*y*z0 - x^108 - x^107*z0 + x^106*z0^2 + x^106*y + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^100*y*z0 + x^101 + x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 + x^95 + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^92*y - x^90*y*z0^2 - x^92 - x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^87 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 + x^82*y*z0^2 - x^84 + x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*z0^2 + x^79*y + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 + x^77 - x^76*z0 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^73 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*z0 + x^70*z0^2 + x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 - x^63*y*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 - x^62*y*z0 + x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 - x^62 + x^61 + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^57*y*z0^2 + x^59 - x^58*z0 - x^56*y*z0^2 - x^58 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^28*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 - x^113*z0 - x^113 - x^112*y + x^112*z0 + x^111*y*z0 - x^110*y*z0^2 + x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 + x^109*z0 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*z0^2 - x^108 - x^107*y + x^106*z0^2 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*z0^2 + x^106 - x^105*y + x^105*z0 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^93 - x^91*y*z0 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^88*y*z0^2 + x^90 - x^89*y - x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 + x^86 - x^85*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y + x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*z0 - x^82*y*z0 - x^81*y*z0 + x^81*z0^2 - x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 - x^76*y*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*y + x^73*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^67*y*z0 - x^67*z0^2 - x^68 + x^67*y + x^67*z0 + x^65*y*z0^2 - x^66*z0 + x^64*y*z0^2 + x^66 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 - x^59*y*z0^2 - x^61 + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^59*y + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 - x^55*y + x^28*y,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^110 - x^108*y*z0 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 - x^107*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 + x^104*y*z0 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 + x^104 - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^96*y*z0 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*y - x^85*y*z0 - x^85*z0^2 - x^86 - x^85*y - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^83*z0^2 + x^83*y + x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^74 - x^73*y + x^73 - x^72*z0 - x^71*z0^2 + x^71*y + x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^67*y*z0 + x^66*y*z0^2 - x^67*y + x^67*z0 - x^65*y*z0^2 - x^66*y - x^65*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^62*y*z0^2 - x^63*z0 + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y + x^60*z0 + x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*y + x^55*y*z0 + x^56 - x^55*y + x^28*y*z0,
 -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^109*y*z0 - x^109*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^105*y - x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y - x^97*y*z0 + x^97*z0^2 + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^94 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^87 - x^85*y*z0 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*z0 + x^83*y*z0 - x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^80*y - x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 + x^76*y*z0 - x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^67 - x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*z0 - x^57*y*z0^2 - x^59 - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^55*y*z0^2 - x^57 + x^56*y - x^55*y*z0 - x^56 + x^28*y*z0^2,
 x^115 + x^114*z0 - x^114 - x^113*z0 + x^112*z0^2 - x^112*y - x^111*y*z0 + x^111*z0^2 + x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 + x^106 - x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^102*y + x^102*z0 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^96*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 - x^80*z0^2 + x^81 + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^76*z0^2 - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*z0^2 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 + x^72 - x^71*y + x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*z0 + x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 + x^66 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y + x^56*z0 + x^29,
 -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y + x^111*y*z0 + x^112 - x^111*y - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*z0^2 - x^109*y - x^109*z0 + x^107*y*z0^2 + x^109 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^106*y + x^105*y*z0 - x^105*z0^2 + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 - x^103*y + x^102*z0^2 + x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^94*y*z0 + x^93*y*z0^2 + x^95 + x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^89*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 - x^80*y*z0^2 - x^81*y - x^80*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*z0^2 + x^80 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^77*y*z0 - x^77*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^74 - x^73*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 + x^71*z0^2 + x^71*y - x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^67*z0^2 + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^65*y*z0 - x^66 + x^65*y - x^65*z0 - x^65 + x^64*y + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^60 - x^59*y - x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^57*z0^2 - x^58 - x^57*y + x^56*z0^2 - x^56*y - x^56*z0 + x^55*y*z0 + x^55*y + x^29*z0,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*y + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109 + x^108*z0 + x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y + x^105*y*z0 + x^104*y*z0^2 + x^106 - x^105*y + x^104*z0^2 + x^103*y*z0^2 - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y - x^103*z0 - x^102*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^99*y*z0^2 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 - x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*z0^2 + x^85 - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^72*y*z0 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^71*y + x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y + x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^58*y*z0^2 - x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^55*y*z0 + x^56 + x^55*y + x^29*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^110*y - x^109*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^104 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*z0^2 - x^102 + x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 + x^98*y*z0^2 + x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 - x^96*y*z0 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 + x^96 + x^94*y*z0 + x^94*y + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^93 + x^92*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 + x^89 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^81*y - x^80*y*z0 + x^79*y*z0^2 - x^80*z0 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^76*z0 - x^76 - x^75*y + x^75*z0 + x^74*y*z0 - x^75 + x^74*z0 + x^73*y*z0 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*z0^2 + x^68*y + x^67*y*z0 - x^66*y*z0^2 - x^67*z0 - x^65*y*z0^2 - x^67 - x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 + x^64*z0 + x^63*z0^2 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^63 - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^58*y*z0 - x^58*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 + x^55*y*z0 + x^56 + x^29*y,
 x^114*z0 + x^113*z0^2 + x^113 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*z0 + x^110*z0^2 - x^110*y + x^110*z0 + x^109*y + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 + x^108 - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^104*y - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*y + x^98*y*z0 + x^98*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^98 + x^97*y + x^95*y*z0^2 + x^96*y - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^88*y*z0^2 + x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*z0 + x^85*y*z0^2 + x^85*y*z0 - x^84*y*z0^2 - x^86 - x^85*y - x^84*y*z0 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^77*z0 + x^76*y*z0 + x^77 - x^76*y + x^75*z0^2 + x^76 - x^75*y - x^73*y*z0^2 + x^74*z0 - x^72*y*z0^2 - x^74 - x^73*y - x^71*y*z0^2 + x^73 + x^72*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 - x^70*z0^2 - x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*z0 - x^67*z0^2 + x^68 - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^63*y*z0 - x^62*y*z0^2 + x^63*y + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^61*y - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*y + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^55*y*z0^2 - x^56*y + x^29*y*z0,
 -x^115 - x^114*z0 - x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*z0^2 - x^108 + x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^103*y*z0 - x^103*z0^2 - x^104 + x^103*y + x^103*z0 - x^103 + x^102*z0 + x^101*y*z0 + x^102 + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^100*z0 - x^99*y*z0 - x^100 - x^99*y + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^93 + x^92*z0 + x^90*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 - x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^74 + x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^68*z0 + x^67*z0^2 - x^68 - x^67*y + x^67*z0 + x^66*z0^2 + x^67 - x^65*y*z0 + x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 - x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^57*y - x^57*z0 - x^57 + x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^29*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 - x^110*y*z0 - x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*y - x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*z0^2 + x^105 - x^103*y*z0 + x^103*z0^2 - x^102*z0^2 + x^103 - x^102*z0 - x^101*z0^2 - x^102 - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^94*y*z0^2 + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*z0^2 - x^94 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y - x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*z0^2 + x^85 - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 - x^81*z0 + x^80*z0^2 + x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*z0 - x^77*z0^2 + x^78 - x^77*y + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^70 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^67*y*z0 + x^66*y*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 - x^66*y + x^65*z0^2 + x^64*y*z0^2 + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*y - x^60*y*z0 - x^59*y*z0 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y + x^57*y*z0 + x^58 - x^57*y - x^56*y*z0 + x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^56 + x^30,
 -x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 + x^101*z0 + x^100*z0^2 - x^101 + x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^92 - x^91*z0 - x^90*z0^2 + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^88*y*z0 + x^89 + x^88*y + x^86*y*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^86 + x^85*z0 + x^83*y*z0^2 - x^85 - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^76 + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y + x^73*y*z0 - x^74 + x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y + x^63*y*z0 - x^63*z0^2 + x^64 - x^63*z0 - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 - x^60*z0^2 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^55*y + x^30*z0,
 -x^115 - x^114*z0 + x^114 - x^113*z0 + x^113 + x^112*y + x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y + x^110*y*z0 + x^111 - x^110*y + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^108*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y + x^101*y*z0 - x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 - x^98*y*z0^2 - x^100 - x^98*y*z0 + x^98*z0^2 - x^98*y + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^93*z0 - x^92*y*z0 + x^91*y*z0^2 + x^93 + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y - x^90*y*z0 + x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^84*y*z0 + x^84*z0^2 - x^84*y + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^80*y*z0 - x^80*z0^2 + x^81 + x^80*y - x^79*y*z0 + x^79*z0^2 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^74*y*z0^2 - x^76 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*z0 + x^71*y*z0 + x^70*y*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*z0^2 + x^67*y*z0^2 + x^68*y - x^68*z0 - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 - x^64*y*z0 + x^63*y*z0^2 - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^63*y + x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^60*z0^2 + x^61 + x^60*z0 + x^59*z0^2 + x^60 - x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^30*z0^2,
 x^115 + x^114*z0 + x^114 - x^113*z0 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^106*y*z0 + x^105*y*z0^2 + x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*y + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y - x^103*z0 - x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 - x^100*z0^2 + x^101 + x^99*y*z0 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^97*y*z0^2 + x^99 - x^96*y*z0^2 - x^98 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^94 - x^93*y + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^83*y*z0^2 - x^84*y - x^83*y*z0 - x^83*z0^2 + x^84 - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^83 + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^77*z0^2 + x^76*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0 - x^74*z0^2 - x^75 + x^74*y + x^74*z0 - x^72*y*z0^2 + x^73*y - x^73*z0 - x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 - x^71 + x^70*y - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*z0 + x^67 + x^65*z0^2 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^62*y*z0^2 + x^63*z0 - x^62*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^55*y + x^30*y,
 -x^115 - x^114*z0 - x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^105 - x^104*y + x^103*y*z0 + x^103*z0^2 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*z0^2 - x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y + x^92*z0 + x^90*y*z0^2 - x^91*y - x^90*z0^2 - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 + x^87 + x^86*y + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 - x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^80*y*z0^2 + x^81*y - x^81*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 + x^79*y*z0 + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^75*z0 + x^74*y*z0 + x^73*y*z0^2 + x^74*z0 - x^73*y*z0 + x^73*y + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y + x^70*y*z0^2 + x^72 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^71 - x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 + x^67*z0^2 + x^68 + x^67*z0 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^64*y + x^64*z0 + x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 + x^62 - x^61*y + x^60*y*z0 - x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^58*y - x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 + x^56*y + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^30*y*z0,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 + x^107*y*z0^2 - x^108*y + x^107*y*z0 + x^108 + x^107*y + x^106*y*z0 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^106 - x^105*y - x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*z0 + x^100*y*z0 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^97*z0^2 + x^97*y + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^93*y - x^92*y*z0 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*y - x^89*y*z0^2 - x^91 - x^90*y + x^89*y*z0 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y - x^85*y - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 - x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^79*y - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^74*y*z0^2 + x^75*y + x^74*y*z0 + x^74*z0^2 - x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^71*y*z0^2 + x^73 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^71 + x^69*y*z0 + x^70 - x^69*y + x^68*y*z0 + x^67*y*z0^2 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 - x^60*y*z0 - x^61 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 + x^30*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y - x^108*y*z0^2 + x^109*y - x^109*z0 - x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*z0^2 + x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^107 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y + x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*z0 + x^96*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^91*y*z0 + x^92 + x^91*y + x^89*y*z0^2 + x^91 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*z0 - x^85*y*z0^2 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*z0 + x^85 + x^84*y + x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0 + x^79*y + x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^77*y - x^76*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^76 + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 + x^71*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^67*z0 + x^66*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 + x^63*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^58*y*z0 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^56*y*z0^2 + x^58 + x^57*y - x^56*y*z0 + x^56*z0^2 + x^57 + x^56*z0 + x^55*y*z0 - x^56 + x^31,
 -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^106 - x^105*z0 - x^104*z0^2 + x^105 - x^104*z0 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^101*z0^2 + x^102 - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 + x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*z0^2 + x^90*y*z0 - x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^84*y + x^83*y*z0 - x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 + x^81*y*z0 - x^80*y*z0^2 + x^82 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*z0 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*z0^2 + x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*z0 - x^75*z0^2 - x^76 + x^75*y - x^75*z0 - x^75 - x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^74 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^70*y*z0^2 - x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^70*z0 - x^69*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^58 + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^31*z0,
 -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^107*y*z0^2 + x^109 + x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 - x^103*y - x^103*z0 + x^102*z0^2 + x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y - x^99*z0^2 - x^100 - x^99*z0 + x^98*z0^2 - x^98*y - x^97*y*z0 + x^97*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^94 - x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^86*y*z0 + x^86*z0^2 - x^87 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 + x^85 + x^84*y - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^80*y*z0 - x^80*z0^2 - x^81 + x^80*y - x^79*y*z0 - x^78*y*z0^2 - x^79*y - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^74*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 + x^70*y*z0^2 - x^70*y*z0 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^63*z0^2 + x^64 + x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^56 + x^31*z0^2,
 -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 - x^111 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^108*y*z0 - x^108*z0^2 + x^108*y + x^106*y*z0^2 - x^107*y + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*z0^2 - x^102*z0 - x^101*y*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^98 - x^97*z0 + x^96*z0^2 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*z0^2 + x^93*y*z0^2 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^93 - x^92*z0 - x^90*y*z0^2 - x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^91 - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^84 - x^83*y - x^83*z0 - x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77 - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 + x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^71 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*z0 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^68 + x^67*y - x^65*y*z0^2 - x^67 - x^66*y - x^65*z0^2 - x^65*y - x^65 - x^64*y - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^62*z0 - x^61*z0^2 - x^62 + x^61*y - x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^56*y*z0 + x^56*z0^2 + x^57 - x^56*y - x^56 - x^55*y + x^31*y,
 x^115 + x^114*z0 + x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*y - x^110*y*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 + x^110 - x^108*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^100*y*z0^2 + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 + x^100 + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^93*y - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 - x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y - x^76*y - x^76*z0 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 + x^72*y - x^72*z0 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^60*z0 + x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y - x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^31*y*z0,
 x^115 + x^114*z0 + x^114 - x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^108*y*z0^2 + x^110 - x^109 - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^103*y*z0 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^101*y*z0 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^96*y*z0^2 - x^98 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*z0 + x^94*y*z0 + x^95 + x^94*y + x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^93*z0 + x^92*z0 + x^92 - x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^86*y*z0 + x^85*y*z0 + x^85*z0^2 + x^86 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*z0^2 - x^84 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 - x^81 - x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^72*y + x^71*y*z0 + x^72 + x^71*y - x^71*z0 - x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^61*y*z0^2 + x^63 - x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^31*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^110*y - x^109*y*z0 - x^110 - x^109*y - x^108*y*z0 - x^107*y*z0^2 + x^109 - x^108*z0 + x^107*z0^2 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^106 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 - x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*z0^2 - x^101 - x^99*z0^2 - x^100 - x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*z0^2 - x^96 + x^95*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^92*y*z0 + x^93 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^89 + x^88*y - x^87*y*z0 + x^87*z0^2 + x^86*y*z0 + x^85*y*z0^2 - x^87 - x^86*y + x^85*y*z0 + x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^84 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^82 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y*z0 - x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^74 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 - x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^69 - x^68*y - x^67*z0^2 - x^68 + x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^64 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^56*y*z0 - x^57 - x^55*y*z0 - x^56 + x^55*y + x^32,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 + x^109*z0^2 - x^110 - x^109*y - x^109*z0 - x^107*y*z0^2 - x^109 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 + x^100*z0 - x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^95 - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^89*y - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*z0 + x^87*y*z0 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*z0 - x^85*z0^2 - x^86 + x^84*y*z0 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*z0 - x^82*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 - x^80 - x^79*y - x^78*y*z0 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 + x^74 - x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^68 + x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*z0 - x^65*y*z0 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 - x^61*y*z0^2 - x^63 + x^62*y + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^58*y*z0 + x^59 - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^32*z0,
 -x^115 + x^113*z0^2 - x^114 + x^112*y + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^108*y*z0^2 + x^110 - x^109*y + x^108*y*z0 + x^109 - x^108*z0 - x^107*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^101 + x^99*y*z0 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 + x^97 + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^95*z0 + x^94*y*z0 + x^95 - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^89*y*z0^2 + x^91 - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*y - x^81*y*z0^2 - x^83 + x^82*y + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y - x^79 + x^78*y - x^77*y*z0 - x^76*y*z0^2 + x^78 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^63*y*z0^2 - x^64*y - x^63*y*z0 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*z0^2 + x^60 + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^59 + x^57*y*z0 - x^57*z0^2 + x^58 - x^56*z0^2 - x^55*y*z0^2 - x^55*y + x^32*z0^2,
 -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^105*y*z0 + x^105*z0^2 - x^105*y + x^105*z0 + x^104*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^102*y*z0 + x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^102 + x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y - x^98*z0^2 + x^97*y*z0^2 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^93 + x^92*z0 + x^91*z0^2 - x^92 - x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*z0 - x^87*z0^2 + x^87*y - x^86*y*z0 + x^86*z0^2 - x^86*y + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*z0^2 - x^83*y + x^83*z0 + x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^81*y - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^78*y*z0 + x^77*y*z0^2 + x^78*y - x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^72 + x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 - x^63*y*z0^2 + x^65 + x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y + x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^58*y*z0^2 - x^59*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^57 + x^56*y + x^55*y*z0 - x^56 + x^55*y + x^32*y,
 x^114*z0 + x^113*z0^2 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*z0 + x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^110 + x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^109 - x^107*y*z0 - x^107*z0^2 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^100*z0 + x^99*y*z0 + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*y + x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 - x^90*y*z0^2 + x^92 + x^91*z0 + x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*y - x^89*z0 - x^89 + x^88*y + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^73*y + x^73*z0 + x^71*y*z0^2 - x^73 + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^69 + x^68*y - x^68*z0 - x^66*y*z0^2 + x^67*y - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 + x^65*z0^2 - x^66 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^57*y*z0^2 + x^59 + x^58*z0 + x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56 - x^55*y + x^32*y*z0,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^110*y - x^109*y*z0 - x^108*y*z0^2 + x^109*y + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*z0 + x^107*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^100*z0 - x^99*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 - x^98*y + x^97*y*z0 - x^97*z0 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^95 + x^94*y + x^94*z0 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 + x^91*y*z0 + x^91*z0^2 - x^92 - x^91*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*z0 - x^89*z0^2 - x^90 - x^89*z0 + x^88*z0^2 - x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*z0 + x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y + x^82*y*z0 - x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y + x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*y*z0 - x^74*z0^2 + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^69*y*z0^2 - x^71 - x^70*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y - x^65*z0 - x^64*y*z0 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^60*y*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^60*y + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 + x^56*y*z0^2 - x^58 + x^57*y + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^32*y*z0^2,
 x^115 - x^113*z0^2 + x^113*z0 + x^113 - x^112*y + x^112*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^103 - x^102*y + x^102*z0 - x^101*z0^2 + x^102 + x^101*y + x^100*y*z0 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 + x^97*y + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^94 + x^92*y*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y - x^88*z0^2 + x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^84*y*z0 - x^85 + x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*z0^2 + x^78*y - x^78*z0 - x^77*z0^2 + x^78 - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^75*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^72 + x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 + x^70 - x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 + x^66*z0^2 - x^67 + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 + x^62*z0^2 - x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^58*y*z0^2 - x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*z0^2 - x^58 - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^56 + x^55*y + x^33,
 -x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^110*z0^2 + x^109*y*z0^2 - x^111 - x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 + x^109 + x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^105*y*z0^2 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*z0 + x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^97*y*z0^2 + x^99 - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 - x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 - x^97 + x^96*y + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^94 - x^93*y + x^92*z0 + x^91*y*z0 - x^91*y + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y - x^89*y*z0 - x^89*z0^2 - x^90 + x^88*y - x^88*z0 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^83*y*z0^2 + x^85 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^82*y*z0 + x^82*y + x^82*z0 + x^80*y*z0^2 - x^82 - x^80*y*z0 + x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 - x^75*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^73*y*z0^2 + x^75 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 + x^71*y*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^70*y*z0^2 - x^70*y*z0 + x^69*y*z0^2 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*z0 - x^68*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^67*y - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y - x^64*z0 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*z0 + x^60*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 - x^56 + x^55*y + x^33*z0,
 -x^115 + x^113*z0^2 + x^114 + x^112*z0^2 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^111*y - x^111*z0 - x^109*y*z0^2 + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*z0 + x^108*y*z0 + x^109 + x^108*z0 - x^106*y*z0^2 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y + x^104*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 + x^100*y - x^100*z0 + x^99*y*z0 + x^98*y*z0^2 + x^100 - x^99*z0 - x^98*y*z0 - x^98*y - x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^95*y*z0 - x^95*z0^2 + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y + x^92*y*z0 - x^93 - x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*y + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^86*y*z0 - x^87 - x^86*y - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^86 + x^85*z0 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^82*y + x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 + x^79*z0^2 - x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^76*y*z0 + x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^72*y*z0^2 - x^73*y - x^73*z0 - x^71*y*z0^2 - x^72*y - x^71*y*z0 - x^70*y*z0^2 - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^61*y*z0 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 + x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^57*y - x^56*y*z0 - x^56*z0^2 - x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*y + x^33*z0^2,
 x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^109*z0 - x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^107*y - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 - x^102*y - x^102*z0 - x^100*y*z0^2 - x^101*y - x^101*z0 - x^100*y*z0 - x^101 + x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^98*z0 - x^97*y*z0 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^94*y*z0^2 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^88*y*z0^2 - x^90 - x^89*z0 - x^88*y*z0 - x^87*y*z0^2 - x^89 - x^88*z0 + x^87*y*z0 - x^88 - x^86*y*z0 + x^86*y - x^86*z0 + x^85*y*z0 + x^86 + x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^79 + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*y - x^74*y*z0 + x^74*z0^2 - x^75 + x^74*y + x^74*z0 - x^74 + x^73*z0 - x^72*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^71*y + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^67*y*z0^2 + x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^67 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 + x^64*y - x^63*y*z0 - x^64 - x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^60*z0^2 - x^59*y*z0^2 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^58*y + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^56*y*z0 - x^56*z0^2 - x^57 - x^55*y + x^33*y,
 -x^115 + x^113*z0^2 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^110*y*z0^2 + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^110 + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^109 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^107 - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 - x^101*z0^2 - x^100*y*z0^2 + x^102 + x^100*y*z0 + x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*z0^2 + x^99 - x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y + x^91*y*z0 + x^91*z0^2 - x^91*y - x^91*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^89*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*z0^2 - x^88 + x^87*y - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y + x^82*y*z0 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y - x^79*y*z0^2 + x^81 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^77*y - x^77*z0 - x^77 + x^76*y + x^75*z0^2 + x^74*y*z0^2 - x^75*z0 + x^73*y*z0^2 - x^75 - x^74*y - x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^59*y + x^59*z0 + x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 - x^55*y + x^33*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*z0 + x^105*y*z0 - x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^103*y*z0 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^99 + x^98*y + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*z0 + x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^92*z0 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^89 + x^88*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 - x^86*z0^2 - x^86*z0 + x^85*y*z0 + x^84*y*z0^2 - x^85*z0 + x^84*z0^2 + x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y + x^83*z0 - x^81*y*z0^2 + x^82*y + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 - x^80*y + x^80*z0 + x^78*y*z0^2 + x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^76*y*z0^2 - x^78 - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^73*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^71*y*z0 - x^71*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 - x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^63*y*z0 - x^63*z0^2 - x^64 - x^63*y + x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^60*z0^2 + x^59*y*z0^2 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y - x^58*y*z0 + x^57*y*z0^2 + x^59 - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^55*y*z0^2 - x^56*z0 - x^56 + x^33*y*z0^2,
 x^115 + x^114*z0 + x^114 + x^113 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^111*y - x^111*z0 - x^110*z0^2 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^105*z0^2 + x^104*y*z0^2 - x^105 - x^104*y - x^103*y*z0 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 + x^101*y + x^100*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 - x^94 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*z0^2 - x^90 - x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y - x^85*y*z0^2 + x^86*y + x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^83*y*z0^2 - x^84*z0 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^78*z0 - x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^75*z0^2 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*z0 + x^71*y*z0 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 - x^60*y*z0^2 - x^62 + x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 + x^58*y + x^58*z0 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^56*y*z0 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 - x^55*y + x^34,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^112*z0^2 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 - x^109*y*z0^2 - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^104*y*z0^2 - x^106 - x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^104*y + x^104*z0 - x^103*y*z0 + x^104 - x^103*y + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^101*y + x^101*z0 + x^101 - x^99*y*z0 - x^99*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y - x^95*y*z0 - x^95*z0^2 + x^96 - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*z0 + x^92*y*z0 + x^93 + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*z0^2 - x^85*y - x^85*z0 + x^84*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^80*y*z0^2 + x^80*y*z0 - x^79*y*z0^2 - x^81 - x^79*z0^2 - x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*z0 - x^74*z0^2 + x^75 - x^74*y + x^73*z0^2 - x^74 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^63*y + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^57*y*z0 - x^57*z0^2 - x^58 + x^57*y + x^56*y*z0 - x^55*y*z0^2 + x^57 + x^56*z0 + x^56 - x^55*y + x^34*z0,
 x^114*z0 + x^113*z0^2 - x^114 - x^112*z0^2 + x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^99*z0^2 - x^98*y*z0^2 + x^99*y + x^99*z0 + x^98*y*z0 + x^99 + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 - x^96*y + x^95*y*z0 + x^94*y*z0^2 + x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 - x^93*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^91*y*z0 + x^90*y*z0^2 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 - x^87*y + x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^85*y*z0 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y + x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*y - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 + x^79 - x^78*y - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^76*z0 + x^75*y*z0 - x^76 - x^75*z0 - x^74*z0^2 - x^75 - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 - x^72 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y + x^67*y*z0^2 + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^68 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^65*z0 + x^64*y*z0 + x^63*y*z0^2 - x^63*y*z0 - x^62*y*z0^2 + x^63*y - x^63*z0 + x^62*z0^2 - x^63 + x^61*z0^2 - x^62 + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^58*y + x^58*z0 - x^57*z0^2 + x^57*y + x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^55*y*z0 + x^56 - x^55*y + x^34*z0^2,
 x^115 + x^114*z0 - x^114 - x^113*z0 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 - x^108*y*z0^2 - x^110 - x^108*y*z0 + x^108*z0^2 - x^108*y + x^108*z0 - x^107*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^105*y*z0 - x^105*z0^2 - x^105*y + x^104*y*z0 + x^104*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^98 - x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^93*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^93 - x^92*y - x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^82*y*z0 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*y + x^78*y*z0 + x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^76 - x^75*y + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^68*y*z0^2 - x^70 + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^65*y*z0^2 + x^67 - x^66*z0 - x^65*y*z0 - x^66 + x^64*y*z0 - x^64*z0^2 - x^64*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*z0^2 - x^63 + x^62*y + x^62*z0 + x^61*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^55*y*z0^2 + x^57 + x^55*y*z0 + x^34*y,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*y + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^107*y*z0^2 + x^109 - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^105*z0 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 - x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^102 - x^100*y*z0 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*z0^2 + x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^96*y + x^96*z0 - x^95*z0^2 + x^96 - x^95*y - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^89*y*z0 - x^88*y*z0^2 + x^89*y - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*z0 + x^83*y*z0 - x^82*y*z0^2 - x^84 - x^82*z0^2 - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^81*y + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 + x^79*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^75 - x^74*z0 - x^72*y*z0^2 + x^74 + x^73*z0 - x^71*y*z0^2 + x^72*y - x^71*z0^2 - x^72 + x^70*z0^2 - x^69*y*z0^2 + x^69*y*z0 + x^69*y - x^69*z0 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^64*y*z0^2 - x^66 + x^65*y + x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*z0^2 - x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^59*y + x^58*z0^2 + x^57*y*z0^2 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 + x^56*y*z0 + x^57 + x^56*y + x^56*z0 + x^56 + x^34*y*z0,
 x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*y - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^104*y*z0 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^102 - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 + x^100*y + x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^95 + x^94 - x^93*y - x^93*z0 + x^92*z0^2 - x^91*y*z0^2 + x^91*y*z0 + x^90*y*z0^2 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*z0 + x^80*z0^2 - x^81 - x^80*z0 + x^79*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^78*z0^2 + x^79 + x^78*y + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^75*y*z0^2 - x^76*y + x^75*y*z0 + x^74*y*z0^2 + x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^75 + x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^71*y + x^71*z0 - x^70*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*z0 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^63 + x^61*z0^2 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 - x^58 + x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^55*y + x^34*y*z0^2,
 x^115 + x^114*z0 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*z0^2 + x^105*y*z0^2 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^101 - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^98*y + x^98*z0 + x^96*y*z0^2 + x^98 + x^95*y*z0^2 + x^97 - x^95*y*z0 - x^95*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^92*y + x^91*z0^2 + x^90*y*z0^2 + x^91*y - x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*z0 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 - x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^76 - x^74*y*z0 + x^75 + x^74*y - x^73*y*z0 + x^73*z0^2 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 + x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^68*z0^2 + x^67*y*z0^2 - x^68*y - x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^63*y*z0^2 - x^64*z0 - x^63*y*z0 - x^64 + x^62*z0^2 - x^63 + x^62*y - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^60*y - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*z0 + x^56*y*z0^2 + x^58 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y + x^56*z0 + x^55*y*z0 + x^56 + x^35,
 -x^115 - x^114*z0 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^109*z0 + x^108*y*z0 + x^109 + x^108*z0 + x^107*y*z0 - x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y - x^100*y*z0^2 + x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*z0 + x^96*y*z0 - x^95*y*z0^2 + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*z0^2 - x^92*y*z0^2 + x^93*z0 - x^92*z0^2 - x^92*y + x^92*z0 + x^91*y*z0 + x^90*y*z0^2 + x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y - x^90*z0 + x^88*y*z0^2 + x^90 - x^89*y - x^88*y*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y + x^87*z0 - x^86*y*z0 - x^87 + x^86*y - x^85*y*z0 + x^84*y*z0^2 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y - x^80*z0^2 - x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*z0 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 - x^75*y*z0^2 + x^77 + x^76*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*z0 - x^72*z0^2 + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^68*y*z0 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 + x^64*y*z0 + x^64*z0^2 + x^65 - x^64*y + x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63 - x^62*z0 + x^61*y - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^58 - x^55*y*z0^2 + x^56*y - x^55*y*z0 - x^56 + x^55*y + x^35*z0,
 -x^115 - x^114*z0 + x^114 - x^112*z0^2 + x^112*y + x^111*y*z0 + x^112 - x^111*y + x^109*y*z0^2 - x^111 - x^109*y + x^109 + x^108*y + x^108*z0 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^106*y + x^106*z0 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^98*y*z0^2 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^96*y*z0 + x^96*y - x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*y*z0 + x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^90*y*z0 + x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*z0 - x^88*z0^2 - x^89 - x^88*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^87 - x^86*y + x^86*z0 + x^85*z0^2 + x^86 + x^85*y - x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*z0^2 + x^82*y + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^80*z0 + x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 - x^78*z0 - x^77*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^64*y - x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*y + x^60*z0 + x^58*y*z0^2 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 - x^56 + x^55*y + x^35*z0^2,
 -x^115 + x^113*z0^2 + x^114 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^112 - x^111*y - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*z0^2 + x^109 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^100 + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^98*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 + x^95*y*z0^2 - x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 + x^93*y*z0^2 - x^95 + x^94*y - x^93*z0^2 + x^93*y + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 - x^91*z0^2 + x^92 + x^91*y + x^91*z0 + x^89*y*z0^2 + x^91 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 + x^85*y + x^84*y*z0 + x^84*z0^2 + x^85 - x^84*z0 - x^83*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^78*y + x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^76*y - x^75*y*z0 - x^76 + x^75*y + x^74*y*z0 + x^74*z0^2 + x^75 - x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 - x^72*y*z0 + x^73 - x^71*y*z0 + x^72 - x^71*z0 - x^70*y*z0 + x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 - x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^62*y*z0 + x^62*z0^2 - x^63 - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*z0 - x^55*y*z0 - x^56 + x^35*y,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 + x^113 - x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^110*y*z0 - x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^105*y*z0 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 + x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 + x^90 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^84 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 - x^75*y*z0^2 - x^77 - x^75*y*z0 + x^74*y*z0^2 - x^75*y - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*z0 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^71 - x^69*z0^2 + x^68*y*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^62*z0 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y + x^35*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 - x^104*y*z0 - x^105 + x^104*y - x^104*z0 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^101*y - x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^97*y*z0 - x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^96*y - x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 + x^94*y - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 - x^90*y*z0^2 + x^92 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^89*z0^2 + x^90 + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^87*y*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 - x^80*z0^2 + x^81 - x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^75*y*z0 + x^75*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^75 - x^74*z0 + x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^71 + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^68*z0^2 - x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^66*y - x^65*y*z0 + x^65*z0^2 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^56 + x^35*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*y + x^110*y*z0 - x^111 + x^110*y - x^110*z0 + x^109*y*z0 + x^110 - x^109*y + x^109 + x^108*y + x^107*y*z0 - x^107*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*z0^2 + x^102*y + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^98 - x^97*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*z0^2 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 + x^92 + x^91*z0 - x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^90 + x^89*y - x^89*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^83 - x^82*y - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 - x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*z0^2 - x^79 - x^78*y + x^77*z0^2 - x^78 - x^77*z0 - x^76*y*z0 - x^77 - x^76*z0 - x^75*z0^2 + x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^71*z0^2 + x^70*y*z0^2 + x^70*y*z0 + x^70*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^67*y + x^67*z0 - x^67 + x^66*z0 + x^65*y*z0 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 + x^56*z0 + x^56 + x^36,
 x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^101*z0 - x^100*y*z0 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*z0 + x^94*z0^2 - x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 - x^89*y*z0 - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^85*y*z0^2 - x^86*y + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*z0 + x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^78*y*z0^2 - x^80 + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^74*y*z0 - x^74*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^72*y + x^72*z0 - x^71*y*z0 + x^72 + x^71*y - x^70*y*z0 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^70 - x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y - x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y - x^60*y*z0^2 - x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^59*y*z0 - x^59*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^56*y - x^55*y*z0 + x^56 + x^36*z0,
 -x^115 + x^113*z0^2 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 - x^110*y*z0^2 - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y + x^109*y*z0 - x^109*z0^2 + x^110 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*z0 + x^105*y*z0^2 - x^107 + x^106*y + x^105*y*z0 + x^105*z0^2 - x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y + x^99*y*z0 - x^99*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 - x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^91 + x^90*z0 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^85*y*z0^2 - x^86*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 + x^84*y + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*y - x^83*z0 + x^82*y*z0 + x^83 - x^82*y - x^81*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^79 - x^78*y - x^76*y*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^74*y*z0^2 - x^76 + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*y - x^69*y*z0 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^66*z0^2 - x^67 + x^66*y + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 + x^63*z0 - x^62*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^61*y + x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^55*y*z0 + x^56 - x^55*y + x^36*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0 + x^107*y*z0^2 - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*z0^2 - x^104*y - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^101*y + x^101*z0 + x^100*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*z0^2 + x^96*z0^2 + x^97 + x^96*z0 - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0 + x^93*z0^2 + x^93*y - x^91*y*z0^2 - x^93 - x^91*y*z0 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*z0^2 + x^89 - x^88*y + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 + x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^81*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y - x^70*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*z0^2 - x^69*y + x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^67*y + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*z0^2 - x^65*y - x^64*y*z0 - x^64*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 + x^62 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^36*y,
 x^115 - x^113*z0^2 + x^114 + x^113*z0 + x^113 - x^112*y + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^110*y - x^109*z0^2 - x^109*z0 + x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*z0 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^104 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y - x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 - x^96*z0 + x^93*y*z0^2 - x^95 - x^93*y*z0 + x^94 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^91*y*z0 - x^90*y*z0^2 + x^91*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 + x^86*z0^2 + x^85*y*z0^2 + x^86*y + x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y - x^82*y*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^77*y*z0^2 + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*z0 - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*z0 - x^73*y*z0^2 - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^72 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^70*y + x^70*z0 + x^69*z0^2 + x^68*y*z0^2 + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*z0 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y + x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 - x^57 - x^56*y + x^56*z0 + x^56 - x^55*y + x^36*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 - x^110 + x^109*y - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*z0^2 - x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^105*y*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^102 - x^101*y + x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 + x^95*z0^2 + x^96 + x^95*y - x^95*z0 + x^95 - x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^84*z0 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^77 + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^75*y + x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^70*y*z0^2 + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 - x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^36*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^110*y*z0 - x^109*y*z0^2 + x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 + x^108*z0^2 - x^109 - x^108*z0 + x^107*y*z0 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 - x^103*y*z0 - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^103 - x^102*z0 - x^101*y*z0 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^95*y*z0 - x^94*y*z0^2 + x^94*y*z0 - x^94*z0^2 - x^95 + x^94*y - x^93*z0^2 - x^93*y - x^93*z0 - x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^88*y - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^86*y*z0 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 - x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*z0 + x^79*y*z0^2 + x^80*y - x^80*z0 - x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^77*y*z0 + x^78 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^73*z0 + x^72*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*z0 + x^64*z0^2 + x^63*y*z0 - x^63*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*y*z0 - x^61*y*z0^2 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 - x^59*y*z0 - x^60 + x^59*y + x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 - x^56*y - x^55*y*z0 + x^55*y + x^37,
 -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 - x^101*z0^2 + x^102 + x^101*y + x^101*z0 - x^100*z0^2 + x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^95*z0^2 - x^94*y*z0^2 + x^95*z0 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 - x^91*y*z0^2 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^85*y*z0 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*z0^2 - x^84*y + x^82*y*z0^2 - x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0 + x^80*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^74 - x^73*y + x^73*z0 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 - x^72 + x^71*y - x^69*y*z0^2 - x^70*y + x^69*y*z0 + x^69*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*y + x^63*y*z0 + x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 + x^58*y*z0^2 + x^60 + x^59*z0 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^56*y*z0^2 + x^58 - x^57*z0 - x^55*y*z0^2 - x^56*y - x^56*z0 - x^56 - x^55*y + x^37*z0,
 x^112*z0^2 - x^112*z0 - x^111*z0^2 - x^112 + x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 + x^105 - x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y - x^102*z0 - x^102 + x^101*y - x^101*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^99*y*z0 - x^100 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 + x^98*y - x^96*y*z0^2 - x^97*y - x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^92*y + x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^88*z0^2 - x^89 - x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^80*y + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^78*y*z0 - x^77*y*z0^2 + x^78*y + x^78*z0 - x^77*y*z0 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^76 + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 - x^73*z0^2 - x^72*z0^2 - x^73 - x^72*y + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^70 + x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*z0^2 + x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^64*y - x^63*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y - x^62*z0 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*z0^2 - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^57*z0 - x^57 + x^56*y - x^55*y*z0 + x^55*y + x^37*z0^2,
 -x^115 - x^114*z0 + x^114 + x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 + x^107*y*z0 + x^107*z0^2 - x^108 - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 + x^106 + x^105*y - x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^100 + x^99*z0 - x^98*y*z0 - x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^97*y - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^93*y - x^92*y*z0 + x^92*y + x^92*z0 + x^91*z0^2 + x^92 + x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 - x^87*y*z0 - x^87*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0 + x^84*y*z0^2 - x^86 - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 - x^84 - x^82*z0^2 + x^83 + x^82*y - x^82*z0 + x^80*y*z0^2 + x^82 - x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^74*y - x^74*z0 + x^73*y*z0 - x^74 - x^73*y - x^73*z0 + x^71*y*z0^2 + x^72*z0 + x^71*y*z0 + x^72 - x^71*y + x^71*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^67*y + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^61*y*z0 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 + x^61 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 - x^55*y*z0^2 - x^57 + x^56*y + x^37*y,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 - x^111 - x^110*y - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y - x^108*y*z0 + x^108*y + x^106*y*z0^2 - x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^106 + x^105*y - x^104*z0^2 - x^104*z0 + x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*y*z0 + x^98 - x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 - x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^89*y*z0 - x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^87*y*z0 + x^86*y*z0^2 - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^84*y*z0 - x^83*y*z0^2 + x^84*z0 + x^84 + x^83*z0 - x^82*z0^2 - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^78*y*z0 - x^78*y - x^78*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^75*z0^2 + x^74*y*z0^2 + x^76 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*y - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 + x^71 - x^70*y + x^70*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*z0^2 + x^67*y*z0^2 + x^68*y - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*z0 - x^67 - x^66*y - x^66*z0 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^64*z0 - x^62*y*z0^2 - x^64 + x^63*z0 - x^62*z0^2 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^58*y*z0^2 + x^59*y - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^57 - x^56*y + x^56*z0 - x^56 + x^37*y*z0,
 x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*z0 - x^103*y*z0 + x^104 - x^103*y + x^102*y*z0 + x^101*y*z0^2 + x^102*y - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*z0^2 - x^97 - x^96*y + x^96 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*z0^2 - x^93*y + x^92*y*z0 - x^91*y*z0^2 + x^93 - x^92*y + x^92*z0 - x^91*z0^2 - x^92 - x^91*y - x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y + x^90 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*z0^2 + x^87 + x^86*z0 - x^85*y*z0 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^84 - x^83*z0 - x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 - x^74*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 - x^70*y - x^69*z0^2 + x^70 + x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^68 - x^67*z0 - x^66*z0^2 + x^66*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^60*z0 - x^59*y*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*z0^2 + x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^37*y*z0^2,
 -x^115 - x^114*z0 + x^114 + x^112*z0^2 - x^113 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 - x^111*y + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^109*y*z0 - x^108*y*z0^2 + x^110 + x^109*y + x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*z0^2 + x^108 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 - x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^95*y - x^95*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 - x^90*y*z0^2 - x^91*y + x^90*y*z0 - x^90*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 - x^89*y - x^88*y*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^87*y*z0 + x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 + x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^82 - x^81*y - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 + x^79*y - x^79 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*z0 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 + x^70*y - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^59*y + x^59*z0 - x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 + x^56*z0 - x^56 - x^55*y + x^38,
 -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 - x^113 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^108*y*z0^2 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 + x^107*y*z0 + x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^103*y*z0 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y + x^96*z0 - x^95*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*y - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 - x^87 - x^86*y - x^86*z0 + x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*y - x^84*z0 - x^82*y*z0 - x^82*z0^2 - x^83 + x^82*y - x^81*y*z0 + x^81*z0^2 - x^82 + x^81*y - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 - x^78*y + x^77*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*z0^2 - x^77 - x^76*y + x^76*z0 - x^75*z0 + x^74*z0^2 + x^73*y*z0^2 + x^74*z0 - x^73*y*z0 + x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 - x^71 - x^69*y*z0 + x^70 + x^69*y - x^69*z0 + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 - x^67*z0 - x^66*z0^2 - x^67 - x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^64*y*z0 + x^64*z0^2 + x^65 + x^64*y + x^64*z0 - x^62*y*z0^2 + x^63*y - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 - x^61 + x^59*y*z0 + x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 + x^57 - x^55*y*z0 - x^56 + x^38*z0,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^104*y - x^104*z0 - x^102*y*z0^2 + x^104 + x^103*y - x^102*y*z0 + x^102*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*z0^2 + x^97*y + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*z0^2 - x^94*y*z0 + x^94*z0^2 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^90*y*z0^2 + x^91*y + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 + x^88*z0 + x^88 - x^87*y - x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^82*z0^2 - x^83 - x^81*y*z0 - x^81*z0^2 - x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^79*z0 - x^78*z0^2 - x^79 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 - x^76*y - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^71*y*z0 + x^71*z0^2 - x^72 - x^71*y + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 - x^66*y + x^65*y*z0 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y + x^57*z0 - x^56*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 - x^56 + x^38*z0^2,
 x^114*z0 + x^113*z0^2 + x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 - x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^104*y*z0 - x^103*y*z0^2 - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 + x^101 + x^100*z0 + x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 + x^98*z0^2 - x^99 + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 + x^95 + x^94*y + x^94*z0 + x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^91 - x^90*y + x^89*z0^2 - x^90 - x^89*y - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y + x^84*y*z0^2 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^83*y*z0 - x^82*y*z0^2 + x^83*z0 - x^82*y*z0 - x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*y + x^74*z0 + x^73*y*z0 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^73 - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^71*y - x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*z0^2 + x^70 + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 + x^68*y - x^68*z0 - x^67*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^63*y*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^63 + x^62*z0 + x^61*y*z0 + x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 - x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y + x^38*y,
 -x^114 + x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^109*y*z0 + x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^108*y + x^108*z0 + x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^105*y*z0 - x^104*y*z0^2 + x^105*y + x^104*y*z0 + x^104*z0^2 + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 + x^101*y*z0^2 + x^103 + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*z0^2 - x^97*y + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 + x^95*y*z0 + x^96 + x^95*y + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^90*y + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88 - x^87*y - x^87*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*z0 - x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 - x^84*z0^2 - x^83*y*z0^2 + x^83*y*z0 + x^83*z0^2 + x^84 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^82*y + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^81 - x^80*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y + x^76 - x^74*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^72*z0^2 - x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*y + x^70*y*z0 - x^70*y + x^69*y*z0 - x^68*y*z0^2 - x^70 - x^69*y - x^68*z0^2 + x^69 - x^68*y + x^67*y*z0 + x^67*z0^2 + x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^66*y + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^65*z0 + x^63*y*z0^2 + x^64*z0 + x^63*y*z0 - x^63*y - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 + x^62 + x^61*y - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^59*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y - x^57*z0^2 - x^56*y*z0^2 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y - x^55*y*z0 + x^55*y + x^38*y*z0,
 -x^115 + x^113*z0^2 + x^113*z0 + x^112*y + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 + x^110*z0^2 + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*y + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^102*z0 + x^101*z0^2 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^94*y + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^89*y*z0 - x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^85*y*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^84*y + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^82*y*z0 - x^82*z0^2 - x^83 - x^82*y - x^82*z0 + x^81*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 - x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 - x^72*y + x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^69*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^66*y + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*z0 + x^61*y*z0 - x^61*y + x^61*z0 - x^59*y*z0^2 - x^61 + x^60*y + x^59*z0^2 + x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^38*y*z0^2,
 x^114*z0 + x^113*z0^2 - x^113*z0 - x^113 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*y*z0 - x^107*y*z0^2 + x^108*y + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*z0^2 - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^96*y*z0^2 - x^98 - x^97*y + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*z0^2 + x^93*y + x^93*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^90*y*z0^2 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*z0^2 - x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 - x^86 + x^85*y - x^85*z0 + x^83*y*z0^2 - x^84*y + x^83*y*z0 + x^82*y*z0^2 + x^84 - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^81*z0 + x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^76 - x^75*y - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 + x^64*y - x^63*y*z0 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^63 + x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 + x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y + x^57*y*z0^2 + x^57*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^39,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^107 - x^106*y + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 + x^101*y*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^101 - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^95*y*z0 - x^95*z0^2 - x^96 + x^95*z0 + x^94*z0^2 + x^95 + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^93 + x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^90*y*z0 + x^90*z0^2 + x^90*y - x^90*z0 - x^89*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*y + x^85*z0^2 - x^86 + x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^83*z0^2 + x^83 - x^82*y - x^81*y*z0 + x^81*z0^2 + x^82 + x^81*y + x^80*y*z0 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^79*y - x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^76 + x^75*y + x^75*z0 - x^74*y*z0 - x^75 - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^74 - x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^71*z0 - x^69*y*z0^2 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^68 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*z0 + x^64*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^56*y*z0^2 + x^58 - x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^39*z0,
 -x^115 - x^114*z0 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y + x^111*y*z0 + x^111*z0^2 - x^112 - x^111*y + x^111*z0 + x^110*y*z0 + x^109*y*z0^2 + x^111 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*y + x^108*z0 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^107 + x^105*y*z0 + x^104*y*z0^2 - x^106 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^95*y*z0 - x^95*z0 + x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^85*y*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*y + x^82*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*z0^2 - x^81 - x^80*y - x^80*z0 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*y + x^78*z0 - x^76*y*z0^2 - x^78 + x^77*y + x^76*y*z0 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^76 - x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^74 - x^73*y - x^72*y*z0 + x^71*y*z0^2 - x^73 - x^72*y + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^61*y - x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*y - x^57*z0 + x^56*y*z0 + x^55*y*z0^2 + x^56*z0 - x^55*y*z0 + x^39*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^110*y*z0 + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 - x^100*y*z0^2 - x^102 - x^101*y - x^100*z0^2 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^100 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 - x^94*y - x^94*z0 - x^93*y*z0 - x^94 + x^93*z0 - x^91*y*z0^2 + x^93 + x^92*y + x^91*z0^2 + x^92 + x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^88*y - x^88*z0 + x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 - x^84 - x^83*y + x^83*z0 - x^81*y*z0^2 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0 + x^81 - x^80*y - x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^76*y + x^75*y*z0 - x^75*y + x^74*y*z0 - x^73*y*z0^2 - x^74*y + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*z0 + x^72*y*z0 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y - x^70*y*z0 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 - x^62*z0^2 - x^63 + x^62*z0 - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^57 + x^56*y + x^55*y*z0 - x^56 + x^55*y + x^39*y,
 -x^114*z0 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y - x^108*y*z0 - x^108*z0^2 + x^109 - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^105*y*z0 - x^104*y*z0^2 + x^106 - x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 + x^102*y*z0 - x^102*y - x^102*z0 - x^102 + x^101*y - x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*z0 - x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^97 + x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*y - x^92*z0 - x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 - x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^88*y + x^86*y*z0^2 + x^87*y + x^87*z0 + x^86*y*z0 - x^87 + x^86*y + x^86*z0 + x^85*z0^2 + x^86 + x^85*y - x^83*y*z0^2 + x^85 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*z0 - x^77*y*z0^2 + x^78*y - x^78*z0 - x^77*z0^2 - x^78 - x^77*y + x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 + x^76*y + x^74*y*z0^2 - x^75*y - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^67 - x^66*y + x^66*z0 + x^65*z0^2 - x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^63*y*z0 - x^62*y*z0^2 - x^64 + x^62*y*z0 - x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 - x^58*y*z0^2 - x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*z0 - x^57*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*y + x^56*z0 + x^56 - x^55*y + x^39*y*z0,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^112*z0^2 - x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^104*z0 - x^103*y*z0 + x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^103 - x^102*y - x^101*z0^2 - x^102 - x^101*z0 - x^100*y*z0 - x^101 - x^100*y - x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^94*y*z0 - x^93*y*z0^2 - x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^93*z0 + x^91*y*z0^2 + x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^89 + x^88*y - x^87*y*z0 + x^86*y*z0^2 - x^88 - x^87*y - x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 + x^85*z0^2 - x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^83*y - x^81*y*z0^2 + x^82*y - x^81*z0^2 + x^81*y + x^81*z0 - x^80*y*z0 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^80 - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^70*z0^2 + x^71 - x^70*y - x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 + x^66*y + x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*y*z0 + x^65 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^63*z0 - x^62*y*z0 - x^63 + x^62*y + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^58*y*z0 + x^58*z0^2 - x^58*y - x^57*y*z0 - x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 - x^55*y + x^39*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 + x^112*y + x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^110 + x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 - x^107*y - x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*y - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^104*y + x^104*z0 + x^103*z0^2 - x^104 + x^103*y - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 + x^101*y*z0 + x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^99*z0^2 - x^99*y + x^99*z0 - x^98*y*z0 + x^97*y*z0^2 - x^98*z0 - x^97*y*z0 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^95*z0^2 - x^96 + x^95*y - x^95*z0 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 - x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^91 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^85 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^79*z0^2 - x^79*y + x^78*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 + x^74*z0^2 + x^74*z0 + x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*z0 + x^71*z0^2 + x^72 - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^57 - x^55*y*z0 + x^40,
 -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y + x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^111*z0 - x^109*y*z0^2 - x^110*y + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*y + x^108*y*z0 + x^108*z0^2 - x^109 - x^108*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y - x^105*y*z0 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y + x^103*z0 - x^101*y*z0^2 - x^101*y*z0 + x^101*z0^2 + x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*y + x^99*y*z0 + x^99*z0^2 + x^99*y + x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 + x^96*y*z0 - x^96*y - x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*z0 + x^94*z0^2 - x^94*y - x^94*z0 + x^92*y*z0^2 - x^94 - x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y - x^89*z0 - x^87*y*z0^2 + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^86 - x^85*y + x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^83*z0 + x^81*y*z0^2 + x^83 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 + x^80 - x^79*y - x^79*z0 - x^78*z0^2 - x^78*y + x^78*z0 - x^77*z0^2 - x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 - x^76 + x^75*y + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^73 - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0^2 + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y - x^66*y - x^65*z0^2 + x^66 - x^65*y + x^65*z0 + x^63*y*z0^2 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 + x^62*y + x^62*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 - x^58 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^56 + x^40*z0,
 -x^115 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^113 + x^112*y - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^106*y + x^106*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*z0 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^102 + x^100*y*z0 + x^99*y*z0^2 - x^100*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*y - x^95*y*z0 - x^94*y*z0^2 - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^90 - x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^86*z0^2 - x^86*y - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 + x^86 - x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 + x^78*z0 - x^78 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^72 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y + x^68*z0 - x^67*z0^2 - x^68 - x^67*y - x^67*z0 + x^66*z0^2 - x^66*y + x^65*y*z0 + x^64*y*z0^2 - x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^62*y*z0 - x^62*z0^2 + x^63 + x^60*y*z0^2 - x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^40*z0^2,
 x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^109*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^108 + x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^105 + x^103*y*z0 + x^103*z0^2 - x^104 - x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^102*y + x^101*y*z0 - x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y - x^94*y*z0 - x^94*z0^2 - x^95 + x^94*y + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^92*z0 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y + x^85*y*z0 - x^84*y*z0^2 + x^86 - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^84*y - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*y + x^82*z0 + x^81*y*z0 + x^80*y*z0^2 + x^81*y + x^81*z0 - x^80*z0^2 + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^75*y*z0^2 - x^76*y + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^70 + x^69*y - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^63 + x^61*z0^2 - x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^56 - x^55*y + x^40*y,
 x^115 - x^114*z0 + x^113*z0^2 - x^112*z0^2 - x^113 - x^112*y + x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^109*y*z0^2 + x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^109*y - x^109*z0 - x^108*z0^2 - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^106*y*z0 + x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^104*y*z0 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*z0 - x^99*y*z0^2 + x^101 - x^99*y - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*y - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*z0^2 - x^94*y - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 - x^92 + x^89*y*z0^2 - x^91 - x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^90 + x^89*y - x^89*z0 - x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^80*y - x^80*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^77*z0^2 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 + x^76 - x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^71*y - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 + x^69*y - x^69*z0 - x^68*y*z0 - x^69 + x^68*y - x^67*y*z0 - x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y - x^65*y*z0 + x^65*z0^2 - x^66 - x^65*z0 + x^64*z0^2 + x^64*y + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*z0 - x^62*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 + x^60*y - x^59*z0^2 - x^58*y*z0^2 - x^60 - x^58*y*z0 - x^57*y*z0^2 - x^58*y + x^57*y*z0 + x^57*z0^2 - x^57*y - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 - x^56 + x^55*y + x^40*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y + x^109*y*z0 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^109 - x^108*z0 - x^107*z0^2 + x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^104*y*z0^2 + x^106 + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^104*z0 - x^103*z0^2 - x^104 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*z0 + x^98*z0^2 + x^99 - x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97 + x^96*y + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 - x^94*y + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^90*y*z0^2 - x^92 - x^91*y - x^90*y*z0 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 - x^86*y*z0^2 + x^88 - x^87*y - x^86*y*z0 - x^86*z0^2 - x^86*y + x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^84*y*z0 - x^83*y*z0^2 - x^85 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*y - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 - x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y - x^76*y*z0 - x^76*y + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y + x^68*z0 + x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^65*y*z0^2 + x^67 - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^63 + x^61*y*z0 - x^61*z0 - x^60*z0^2 + x^61 - x^59*y*z0 + x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^58 + x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^56*z0 + x^56 - x^55*y + x^40*y*z0^2,
 -x^114*z0 - x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 + x^111*y - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*y + x^108*z0^2 - x^107*y*z0^2 + x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0 - x^101*y*z0^2 + x^103 - x^102*z0 + x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^97 - x^95*y*z0 - x^96 + x^95*y - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 - x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^88*y - x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 + x^84*y - x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y + x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^79*y*z0 - x^79*z0^2 + x^80 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*z0^2 + x^77 + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*z0 + x^74*z0^2 - x^74*y + x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 - x^73*y + x^72*z0^2 + x^71*y*z0^2 + x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 - x^70*y*z0 - x^70*y - x^70*z0 + x^69*y*z0 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 - x^68*y + x^67*y*z0 - x^68 - x^67*z0 + x^65*y*z0^2 + x^67 + x^65*y*z0 - x^64*y*z0 - x^64*z0^2 - x^64*z0 - x^63*y*z0 + x^63*z0^2 + x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^62*y - x^62*z0 + x^61*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^58 + x^57*z0 - x^56*y*z0 + x^57 - x^56*z0 - x^55*y*z0 + x^56 + x^41,
 x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y - x^109*z0 + x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 + x^105 - x^104*z0 + x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 - x^101 + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^98*y*z0 + x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^90*y + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^83*y + x^82*y*z0 - x^82*z0^2 + x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^77*y + x^77*z0 + x^76*y*z0 + x^77 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^75*z0 + x^74*z0^2 - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^72*y + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*y - x^68*z0^2 - x^67*y*z0^2 - x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 + x^65*y*z0 - x^64*y*z0^2 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y + x^63*y*z0 - x^63*y + x^62*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^56*y*z0 - x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 + x^55*y + x^41*z0,
 x^115 + x^114*z0 + x^114 + x^113*z0 + x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*y*z0 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^109 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^105*y*z0^2 + x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*z0^2 + x^102*y + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*y - x^100*y*z0 - x^100*z0^2 - x^101 - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^99*z0 - x^98*z0^2 + x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*z0 + x^96*y*z0 + x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^95 + x^93*y*z0 - x^94 + x^93*z0 + x^91*y*z0^2 + x^93 - x^91*y*z0 + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^90 - x^89*y - x^89*z0 - x^88*z0^2 - x^89 - x^87*y*z0 - x^87*z0^2 + x^88 - x^87*y - x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^86 + x^85*y - x^84*y*z0 + x^83*y*z0^2 + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 - x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 - x^81 + x^80*y + x^79*y + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*z0 + x^76*y*z0^2 - x^78 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^74*y*z0^2 - x^75*z0 + x^74*y*z0 + x^73*y*z0^2 - x^75 - x^73*y*z0 - x^72*y*z0^2 - x^73*y + x^73*z0 + x^71*y*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*y - x^63*z0 - x^62*z0^2 - x^63 - x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 - x^60*y*z0 + x^61 + x^60*z0 - x^59*y*z0 - x^59*y + x^59*z0 + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 + x^56*z0 - x^55*y*z0 - x^56 + x^41*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 - x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y + x^101*z0 - x^100*y*z0 + x^100*y - x^99*z0^2 - x^100 + x^99*y - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 - x^97 + x^96*y + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 + x^94*y - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*z0 + x^93 - x^92*y + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 - x^89*y*z0^2 + x^90*y + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y + x^88*z0^2 - x^87*y*z0^2 + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^87 - x^86*z0 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*y + x^80*y*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 + x^80*z0 + x^79*z0^2 - x^79*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^76*y*z0^2 + x^78 - x^77*y - x^76*z0^2 + x^75*y*z0^2 + x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^75 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*z0 - x^71*y*z0 - x^72 - x^70*y*z0 - x^70*z0^2 + x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 - x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 + x^65*y - x^65*z0 - x^64*y*z0 - x^62*y*z0^2 + x^64 + x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^61*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 - x^59*y*z0 - x^58*y*z0^2 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^59 + x^58*y - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 + x^55*y*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 + x^55*y + x^41*y,
 -x^115 - x^114*z0 + x^114 - x^113*z0 + x^113 + x^112*y + x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^111 - x^110*y - x^110*z0 + x^108*y*z0^2 - x^109*y - x^108*y*z0 + x^108*z0^2 - x^109 + x^108*y + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^107*y + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*y*z0 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 - x^102*z0 + x^101*z0^2 - x^100*y*z0^2 + x^102 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*y - x^99*z0 - x^98*y*z0 - x^97*y*z0^2 - x^99 - x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 + x^96 - x^95*y - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y - x^93*z0^2 + x^93*y + x^93*z0 - x^92*y*z0 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y - x^91*z0 + x^90*z0^2 + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*z0 + x^85*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^84*y + x^84*z0 - x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 - x^83 - x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*z0 - x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 - x^78*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y - x^76*y*z0 - x^77 + x^76*y - x^76*z0 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*z0^2 - x^75 + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^73*y + x^72*y*z0 + x^71*y*z0^2 - x^73 - x^71*y*z0 + x^72 - x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 - x^68*z0^2 + x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y - x^64*y*z0 - x^64*z0^2 - x^65 - x^64*y - x^62*y*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^59*y*z0^2 + x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y - x^59*z0 - x^58*z0^2 - x^59 - x^58*y + x^56*y*z0^2 - x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*z0 + x^56 + x^55*y + x^41*y*z0,
 x^114*z0 + x^113*z0^2 + x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 + x^110 - x^109*y - x^109*z0 + x^108*y*z0 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*y*z0 - x^104*y*z0^2 - x^106 + x^105*y + x^104*y*z0 - x^103*y*z0^2 + x^105 - x^104*y - x^103*y*z0 - x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^103 - x^102*z0 - x^102 + x^101*y - x^101*z0 + x^100*z0^2 - x^101 - x^100*y + x^99*z0^2 + x^99*y + x^98*y*z0 - x^98*z0^2 + x^97*y*z0 - x^96*y*z0^2 + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*z0 + x^95*y*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*y - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^87 + x^85*y*z0 - x^85*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83*z0 - x^82*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^81*y + x^81*z0 - x^80*z0^2 - x^79*y*z0^2 - x^80*y + x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*z0^2 + x^73 + x^72*y - x^72*z0 - x^72 - x^71*y + x^70*y*z0 - x^69*y*z0^2 + x^70*z0 + x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*z0 - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y + x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^62*y*z0 - x^62*z0^2 - x^63 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 - x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 - x^56*y*z0^2 - x^58 + x^57*y + x^56*y*z0 - x^56*z0 - x^56 + x^55*y + x^41*y*z0^2,
 -x^114*z0 - x^113*z0^2 + x^113*z0 - x^113 - x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^107*y*z0^2 - x^109 + x^108*y - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^106 - x^105*y - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*z0 + x^103*y*z0 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*y + x^102*z0 + x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 - x^100*y + x^99*y*z0 - x^99*y + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^95*y*z0^2 - x^97 + x^96*z0 - x^94*y*z0^2 - x^96 - x^94*y*z0 + x^94*z0^2 + x^95 + x^94*y + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y + x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 - x^91*z0 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^89 + x^88*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y - x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y + x^69*y*z0 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 - x^67*y*z0 + x^68 - x^67*y - x^66*z0^2 + x^65*y*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^65*y + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 - x^58*y*z0 + x^59 + x^58*y + x^58*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^57 - x^56*z0 - x^55*y*z0 + x^55*y + x^42,
 -x^115 - x^114*z0 + x^114 + x^112*z0^2 + x^113 + x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 - x^111*y - x^109*y*z0^2 - x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^109*y + x^109*z0 + x^108*z0^2 - x^109 - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105*z0 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^99 - x^98*y - x^96*y*z0^2 + x^97*y - x^96*y*z0 - x^96*z0^2 - x^96*y + x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^94*y*z0 - x^94*y - x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 - x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*z0^2 - x^92 + x^91*z0 + x^89*y*z0^2 + x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 + x^90 - x^89*z0 - x^87*y*z0^2 + x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^85*y*z0^2 + x^87 + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y - x^84 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 + x^77*y - x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^74*z0^2 + x^75 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*z0 + x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*z0 + x^69*z0^2 + x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*z0^2 - x^68*y - x^68*z0 + x^67*y*z0 + x^68 - x^67*y + x^67 - x^65*y*z0 - x^65*z0^2 + x^66 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^62*y - x^62*z0 - x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^59*y*z0^2 - x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*z0 - x^56*y*z0 - x^56*z0^2 + x^57 + x^55*y*z0 + x^42*z0,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^113 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^111 - x^110*y - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^106*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 + x^99 - x^97*y*z0 - x^96*y*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 + x^97 + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^95*y + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^88*y*z0 - x^88*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^86*y*z0 - x^86*z0^2 - x^86*y + x^85*y*z0 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^83*y + x^83 + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^76*z0 + x^74*y*z0^2 - x^76 + x^75*y + x^74*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^71*y*z0^2 - x^73 + x^72*z0 + x^71*y*z0 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 - x^69*y*z0 - x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^68*y - x^68*z0 + x^67*z0^2 + x^66*y*z0^2 - x^67*y + x^67*z0 + x^66*z0^2 - x^67 + x^65*y*z0 - x^65*z0^2 + x^66 + x^65*y + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*y + x^62 + x^61*y + x^61*z0 + x^60*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^58*y - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56*y + x^56 + x^55*y + x^42*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^108*y*z0^2 - x^110 + x^109*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*y*z0 + x^107 - x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^106 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 + x^102*y*z0 + x^102*z0^2 + x^103 - x^102*z0 + x^101*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 - x^95*y*z0^2 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 - x^89*y*z0 - x^90 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^89 - x^87*z0^2 + x^88 + x^87*y + x^85*y*z0^2 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y - x^84*z0^2 + x^85 + x^83*y - x^82*y*z0 + x^82*z0^2 - x^82*y - x^82*z0 + x^81*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 + x^77*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^77 + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y - x^74*z0^2 + x^73*y*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^70*y - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 - x^68*y + x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^65 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*z0 - x^62*z0^2 + x^63 - x^62*z0 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^59*y*z0^2 + x^60*y - x^60*z0 + x^58*y*z0^2 - x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^58 + x^57*y - x^57*z0 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^42*y,
 x^115 - x^113*z0^2 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 + x^108*y*z0 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 - x^104*z0^2 + x^105 - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*z0 - x^102*y*z0 + x^103 - x^102*y + x^101*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^100*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^96*y*z0 + x^95*y*z0^2 - x^97 + x^96*y + x^95*z0^2 + x^94*y*z0^2 - x^95*y + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 + x^93*y - x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^89*y*z0 - x^89*z0^2 + x^89*z0 + x^88*y*z0 + x^88*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^86*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 + x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^76*y + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*y*z0 + x^74*y + x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^69*y*z0^2 + x^69*y*z0 + x^68*y*z0^2 + x^69*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^66*z0^2 - x^65*y*z0^2 + x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*z0 - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^61*z0^2 + x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^61 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*y + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^42*y*z0,
 x^115 + x^114*z0 - x^113*z0 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 + x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^98*y*z0 - x^99 - x^98*z0 + x^97*y*z0 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*y + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^93*y + x^92*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*y*z0 + x^83*y + x^83*z0 - x^82*z0^2 + x^83 - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 + x^75*y*z0^2 - x^76*y - x^76*z0 - x^75*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^75 - x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*z0 + x^71 - x^70*y - x^69*z0^2 + x^70 + x^69*y + x^69 + x^68*y - x^68*z0 + x^67*y*z0 + x^66*y*z0^2 + x^66*z0^2 + x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^65*y + x^65*z0 + x^63*y*z0^2 - x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*z0^2 - x^59*y + x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x^42*y*z0^2,
 x^115 - x^113*z0^2 + x^113*z0 + x^112*z0^2 + x^113 - x^112*y - x^112*z0 + x^111*z0^2 + x^110*y*z0^2 - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*z0 + x^108*y*z0 + x^107*y*z0^2 + x^109 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*y*z0 + x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 - x^104*y*z0 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^103 - x^101*y*z0 - x^102 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^99*y - x^99*z0 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 - x^98 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*z0 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 + x^89*y*z0^2 + x^90*y + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 - x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 + x^86*y*z0 - x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 + x^85*y - x^85 + x^83*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 - x^81*y*z0^2 - x^83 + x^82*y + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*y + x^79*z0 - x^78*y*z0 + x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^64 + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^62*y - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*z0 - x^55*y*z0 + x^56 + x^43,
 -x^115 + x^114*z0 - x^113*z0^2 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^110*z0^2 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^107*y*z0^2 - x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 + x^103*z0^2 + x^104 - x^103*y - x^103 + x^102*y + x^102*z0 - x^100*y*z0^2 + x^102 - x^101*y - x^100*z0^2 - x^100*y - x^100*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^98*y*z0 - x^98*z0^2 + x^98*y - x^98*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*z0^2 - x^94*y*z0^2 + x^95*z0 - x^94*z0^2 - x^95 + x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*y*z0 - x^92 - x^90*y*z0 - x^90*z0^2 - x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y - x^89*z0 + x^88*y*z0 - x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^85*y + x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 + x^83*y - x^82*y*z0 + x^83 - x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^81*y - x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^79 + x^78*y - x^78*z0 - x^77*z0^2 + x^78 - x^77*y - x^77*z0 + x^76*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^75*y + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0 + x^67*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*z0 + x^65*z0^2 + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y - x^62*z0 - x^60*y*z0^2 + x^62 + x^61*y - x^60*z0^2 - x^61 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y + x^56*y*z0^2 + x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 + x^43*z0,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y - x^107*z0 + x^106*z0^2 + x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*z0 - x^103*y*z0^2 - x^105 + x^104*z0 + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^102*y*z0 - x^102*z0^2 - x^103 - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^101 - x^100*y - x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^96*y*z0^2 + x^97*y - x^97*z0 + x^96*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^91*y*z0^2 + x^93 - x^91*z0^2 - x^92 - x^91*y + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^89*y*z0 + x^88*y*z0^2 + x^90 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*z0^2 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*z0 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y + x^75*y*z0^2 + x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*y - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 - x^73*y - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*y*z0 + x^70*y - x^69*z0^2 - x^69*y - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 - x^65*y*z0^2 + x^65*y*z0 - x^65*z0^2 + x^65*y + x^64*y*z0 - x^64*z0^2 + x^65 - x^64*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^59*y*z0 - x^59*z0^2 - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^58 - x^56*y*z0 + x^55*y*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^43*z0^2,
 x^114*z0 + x^113*z0^2 - x^114 + x^112*z0^2 - x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y - x^111*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^105*y - x^104*y*z0 - x^104*z0^2 + x^105 - x^103*y*z0 - x^103*z0^2 + x^103*y - x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*z0^2 + x^98 - x^97*y - x^96*y*z0 + x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 + x^90*y*z0^2 - x^92 + x^91*y - x^91*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*y + x^86*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^84*y*z0 + x^84*z0^2 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^84 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 + x^78*y*z0^2 - x^79*y + x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 - x^78 - x^77*y + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^75*y*z0 - x^75*z0^2 - x^75*y + x^75*z0 - x^74*y*z0 - x^74*z0^2 - x^75 - x^74*y + x^73*y*z0 - x^72*y*z0^2 + x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^73 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*z0 - x^69*z0^2 - x^70 - x^69*y - x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y + x^67*z0 + x^67 + x^66*y + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 - x^62*z0^2 + x^63 - x^62*y - x^61*y*z0 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 + x^60*y + x^60*z0 + x^59*z0^2 + x^60 + x^59*z0 - x^58*y*z0 - x^58*z0^2 - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^58 + x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^43*y,
 -x^115 - x^114*z0 + x^114 - x^113*z0 - x^112*z0^2 + x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 + x^108 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 + x^106*y - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 - x^104*z0^2 - x^104*y + x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^97*y*z0^2 + x^98*y + x^96*y*z0^2 - x^98 - x^96*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 - x^89*y*z0^2 - x^90*y + x^90*z0 - x^89*z0^2 + x^90 - x^89*y - x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 - x^87*y*z0 - x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^86*y - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*y*z0 - x^80 + x^79*y - x^79*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^74 + x^73*y + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^70*y*z0^2 + x^71*y - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^68*y*z0^2 - x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 + x^66*z0^2 + x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 - x^62*y*z0^2 + x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^62*z0 - x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 - x^59 + x^58*z0 - x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^56*z0 + x^55*y*z0 - x^56 + x^43*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 + x^109*y - x^108*z0^2 - x^109 + x^108*y - x^106*y*z0^2 + x^108 - x^106*y*z0 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*y + x^102*z0^2 - x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0 + x^101 + x^100*y + x^100*z0 + x^99*y*z0 - x^100 + x^99*z0 + x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 + x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y + x^90*z0^2 - x^89*y*z0^2 - x^89*y*z0 + x^88*y*z0^2 + x^89*y - x^89*z0 + x^87*y*z0^2 + x^89 - x^88 - x^87*y + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*y*z0 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y - x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*y - x^81*y*z0 + x^80*y*z0^2 - x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 + x^72*y*z0^2 - x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^72*z0 + x^71*y*z0 - x^70*y*z0^2 - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 + x^68 - x^67*y + x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 - x^63*y*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^62*y*z0 - x^62*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*z0 - x^58*y*z0 + x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^57 + x^56*y - x^56*z0 - x^55*y*z0 - x^56 - x^55*y + x^43*y*z0^2,
 x^115 + x^114*z0 - x^114 + x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 + x^111*y - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y - x^105*y*z0^2 - x^106*y + x^105*y*z0 - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^104*y - x^104*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y + x^103*z0 + x^102*z0^2 + x^103 - x^102*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 - x^100*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^99 - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^97*z0 + x^95*y*z0^2 - x^97 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^94*y*z0 + x^93*y*z0^2 + x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0 - x^92*z0^2 - x^93 + x^91*y*z0 - x^90*y*z0 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 + x^87*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 + x^87 + x^86*y + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^84 + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*y + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^78*y*z0^2 + x^80 + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 + x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^75*z0^2 + x^74*y*z0^2 - x^76 + x^75*y + x^75 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^73*y + x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*z0^2 - x^72 + x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^71 - x^70*y + x^70*z0 + x^69*y*z0 - x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^68*y + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*z0^2 + x^66 - x^65*y - x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 - x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 + x^60*y*z0^2 - x^61*y - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60*y + x^60*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^57*y*z0^2 - x^59 - x^58*y + x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*y - x^57*z0 + x^55*y*z0^2 - x^57 + x^56*z0 + x^56 + x^44,
 x^115 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^112*y + x^111*z0^2 + x^110*y*z0^2 + x^111*y + x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^108 + x^107*z0 + x^106*y*z0 + x^106*z0 + x^104*y*z0^2 - x^106 - x^105*z0 - x^104*z0^2 - x^105 + x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y - x^103*z0 - x^101*y*z0^2 - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y - x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^99*y - x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^97*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*z0 + x^94*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 + x^92 - x^91*z0 - x^90*z0^2 + x^89*y*z0^2 + x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^88*y*z0^2 + x^90 + x^89*y - x^88*y - x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y - x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 + x^76*y*z0 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^75 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^71 - x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^70 + x^69*y - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^67*z0^2 - x^68 - x^66*z0^2 - x^65*y*z0^2 + x^66*z0 + x^65*y*z0 + x^65*z0^2 - x^66 - x^65*z0 + x^64*y*z0 + x^64*y - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y - x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*z0^2 + x^62 + x^61*y - x^61*z0 + x^60*y*z0 - x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 - x^59*z0^2 - x^60 - x^59*y + x^59*z0 - x^57*y*z0^2 + x^58*y + x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 - x^56 + x^44*z0,
 -x^115 - x^114*z0 - x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 + x^110*y - x^110*z0 - x^109*y*z0 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^109 - x^108*z0 + x^107*y*z0 - x^108 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 + x^105*z0^2 - x^105*z0 - x^103*y*z0^2 - x^104*z0 - x^103*y*z0 + x^103*y + x^102*y*z0 - x^103 - x^102*y + x^101*y*z0 + x^101*y + x^101*z0 - x^100*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y - x^95*z0^2 - x^94*y*z0^2 + x^95*z0 - x^94*y*z0 + x^95 - x^94*y - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*y + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^86*z0 + x^84*y*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y - x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83*z0 - x^82*z0^2 + x^83 + x^81*z0^2 + x^81*y - x^81 + x^80*y + x^80*z0 + x^78*y*z0^2 + x^79*y - x^78*y*z0 - x^77*y*z0^2 - x^79 + x^77*y*z0 + x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*y + x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*z0 - x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*z0^2 - x^68*y*z0^2 - x^70 - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y - x^67*y*z0 - x^67*y + x^66*z0^2 + x^66*z0 + x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*z0^2 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 - x^60*y*z0^2 + x^62 + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 - x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*y - x^56 - x^55*y + x^44*z0^2,
 -x^112*z0^2 - x^112 - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*z0 + x^109*z0^2 + x^110 + x^109*y + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*z0^2 + x^105*y*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^104*y - x^103*y*z0 - x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y - x^101*y*z0 - x^101*z0 - x^100*y*z0 + x^100*z0^2 - x^101 + x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^94*y*z0 - x^95 - x^94*y + x^93*z0^2 + x^92*y*z0^2 + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^88 - x^87*y - x^87*z0 - x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^84 + x^82*y*z0 + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 + x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^74*y*z0^2 + x^76 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^74*z0 + x^73*y*z0 + x^74 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y + x^71*y*z0 + x^71*z0^2 - x^71*y + x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*z0 - x^68*z0^2 - x^69 + x^68*z0 + x^67*y*z0 - x^66*y*z0^2 + x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^62*y - x^61*y*z0 + x^61*z0^2 - x^62 + x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^59*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 + x^55*y + x^44*y,
 x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 - x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 - x^110*y*z0 + x^110*z0^2 - x^111 + x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^108*y - x^108*z0 + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*z0^2 + x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y + x^102*y*z0 + x^102*z0^2 + x^103 - x^102*y + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^100*y - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*z0 + x^93*y*z0 - x^92*y*z0^2 - x^93*y + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y + x^91*y*z0 + x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^91 - x^90*y + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*z0 - x^86*y*z0 + x^85*y*z0^2 + x^87 - x^86*y + x^85*y*z0 - x^86 - x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^83*y + x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^81*z0^2 + x^80*y*z0^2 + x^81*z0 + x^79*y*z0^2 + x^81 - x^80*y - x^80*z0 + x^79*z0^2 + x^80 + x^79*z0 - x^78*y*z0 + x^79 + x^78*y - x^78*z0 + x^77*y*z0 - x^78 - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*y + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0 + x^69*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^65 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*z0^2 + x^62*y + x^62*z0 - x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 - x^61 + x^60*y + x^59*y*z0 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 + x^58*y*z0 + x^58*z0^2 + x^58*y - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^57*y + x^56*y*z0 + x^56*z0^2 - x^55*y + x^44*y*z0,
 -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 - x^109*y*z0 - x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^107 + x^105*y*z0 + x^104*y*z0^2 + x^104*y*z0 + x^103*y*z0 + x^102*y*z0^2 - x^104 + x^103*y - x^103*z0 - x^101*y*z0^2 + x^103 + x^102*y - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 - x^96*y*z0^2 - x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^92*z0 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 - x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^89 - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y + x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y + x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 + x^83*y - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y + x^77*y*z0^2 - x^79 + x^78*z0 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^76*y - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 + x^73*y*z0 + x^74 + x^73*y + x^73*z0 - x^72*y*z0 + x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 + x^69 + x^68*y + x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^65*y + x^65*z0 - x^64*z0^2 - x^64*y - x^64*z0 - x^64 + x^63*y - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*y*z0 + x^60*y*z0^2 + x^62 + x^60*z0^2 + x^61 + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 + x^58 + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^56*z0 - x^55*y*z0 + x^55*y + x^44*y*z0^2,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y - x^108*y*z0 + x^107*y*z0^2 - x^109 + x^108*z0 + x^107*y*z0 + x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*z0 - x^100*y*z0^2 - x^101*y + x^100*z0^2 - x^101 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 - x^94 + x^93*y - x^92*y*z0 + x^91*y*z0^2 + x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y - x^90*y*z0 + x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 + x^89 + x^88*y - x^88*z0 - x^88 + x^87*y - x^87*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*y + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 - x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^73*y*z0^2 - x^75 - x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^73*z0 + x^71*y*z0^2 + x^72*y + x^72*z0 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*z0 + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y - x^64*z0 - x^63*y*z0 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 - x^60*y + x^59*z0^2 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*z0 - x^58 + x^55*y*z0^2 - x^57 + x^56*y - x^56 + x^55*y + x^45,
 x^115 - x^113*z0^2 - x^114 + x^113*z0 + x^112*z0^2 + x^113 - x^112*y + x^112*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^110 + x^109*y - x^108*y*z0 + x^107*y*z0^2 + x^108*y + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 - x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^102 - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 + x^93*y*z0 + x^94 + x^93*y - x^93*z0 + x^92*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*y - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^86*y + x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 + x^83*y - x^83*z0 - x^82*y*z0 + x^83 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^80*y - x^80*z0 - x^79*y*z0 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^77*y*z0^2 + x^79 + x^78*y + x^77*y*z0 + x^77*z0^2 + x^77*y + x^77*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y + x^76*z0 - x^74*y*z0^2 - x^76 - x^75*y - x^75*z0 - x^74*z0^2 - x^74*y + x^72*y*z0^2 + x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^70*y*z0^2 + x^72 + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^68*y*z0 + x^67*y*z0^2 + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^66*z0^2 + x^65*y*z0^2 - x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y*z0 + x^64*z0^2 + x^65 - x^64*z0 + x^63*z0^2 + x^64 + x^63*y + x^63*z0 + x^62*y*z0 - x^62*z0^2 - x^62*y - x^62*z0 - x^61*z0^2 + x^62 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 - x^59*y - x^59*z0 + x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^56*y*z0 - x^56*z0^2 + x^57 - x^56*y - x^55*y*z0 + x^45*z0,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^113*z0 + x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*y - x^109*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^109 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^103*z0^2 + x^104 - x^103*z0 + x^102*z0^2 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 - x^97*z0 - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*z0 - x^91*y*z0 + x^91*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 + x^89*y - x^89 + x^88*z0 + x^87*z0^2 - x^88 - x^87*y + x^87*z0 - x^85*y*z0^2 - x^86*y + x^86*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^81 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^79 - x^78*z0 - x^77*y*z0 - x^78 + x^77*y + x^76*z0^2 + x^77 + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 + x^76 - x^75*y - x^73*y*z0^2 + x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^71*y - x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 + x^69*y*z0 + x^69*z0^2 - x^69*y + x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 + x^69 - x^68*z0 - x^67*z0^2 - x^68 + x^67*y - x^66*z0^2 + x^67 - x^66*y + x^66*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y + x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^60*y + x^60*z0 + x^58*y*z0^2 + x^60 - x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^57*y*z0 - x^57*z0^2 + x^57 + x^56*y - x^56*z0 - x^56 - x^55*y + x^45*z0^2,
 x^114*z0 + x^113*z0^2 + x^112*z0 - x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*z0 - x^111 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^108*y*z0 - x^108*z0^2 + x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*z0^2 - x^106 + x^105*y + x^105*z0 + x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^104 - x^103*z0 - x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 - x^101*y*z0 - x^102 - x^100*y*z0 - x^99*y*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 - x^94 + x^92*z0^2 - x^92*y - x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^90*y - x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^88*y*z0 + x^88*z0^2 + x^89 + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^87*y - x^87*z0 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y + x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*z0^2 + x^81*y*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^80*z0^2 + x^79*y*z0^2 - x^81 - x^79*y*z0 + x^79*z0^2 - x^80 - x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 - x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^67*y*z0^2 - x^68*z0 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*y + x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^63*y*z0 - x^63*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^61*y*z0^2 + x^63 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y - x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 + x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^56 - x^55*y + x^45*y,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 + x^110*y*z0 + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 + x^105*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*z0 - x^103*z0^2 - x^104 - x^103*y + x^103*z0 - x^102*z0^2 + x^103 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^100 - x^99*y + x^99*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*z0^2 - x^95*y*z0^2 - x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*z0^2 + x^94 + x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^90*y*z0^2 - x^92 - x^91*z0 + x^89*y*z0^2 - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*y*z0 - x^86*z0^2 - x^87 + x^86*y - x^86*z0 - x^85*y*z0 + x^84*y*z0^2 - x^86 + x^85*y - x^84*z0^2 - x^83*y*z0^2 + x^85 - x^83*y*z0 - x^83*z0^2 + x^84 - x^83*y + x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^82*y + x^81*y*z0 + x^82 + x^81*z0 - x^79*y*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*z0 - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 - x^77 - x^76*y - x^75*y*z0 + x^75*z0^2 + x^76 + x^75*y - x^75*z0 - x^74*y - x^73*y*z0 + x^72*y*z0^2 - x^74 + x^73*y - x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^68*y - x^68*z0 - x^67*z0^2 - x^68 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^64*y*z0^2 - x^64*z0^2 + x^63*y*z0^2 + x^64*z0 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^60*z0 + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^56*y - x^55*y*z0 + x^56 - x^55*y + x^45*y*z0,
 -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^110*z0 - x^109*y*z0 + x^108*y*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 + x^109 + x^107*y*z0 + x^107*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^104*y*z0^2 - x^106 + x^105*z0 - x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^104 + x^103*y + x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 - x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^101*y + x^100*z0^2 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^97*y*z0^2 - x^99 - x^97*y*z0 + x^97*z0^2 + x^98 + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^96*z0 - x^95*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*z0 - x^91*y*z0^2 + x^93 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y - x^90*y*z0 - x^90*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 + x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 + x^88*y - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^86 + x^85*y - x^85*z0 - x^83*y*z0^2 - x^84*y - x^82*y*z0^2 + x^84 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*y - x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^76*y*z0^2 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 + x^76*y + x^75*y*z0 - x^74*y*z0^2 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 - x^73*y*z0 + x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 + x^71*y*z0 - x^70*y*z0^2 + x^71*y - x^71*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*y - x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 - x^68 + x^67*y - x^66*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*z0 + x^63*y*z0^2 - x^65 + x^64*y + x^62*y*z0^2 - x^64 + x^63*y - x^62*z0^2 + x^61*y*z0^2 + x^62*z0 + x^61*y*z0 - x^62 - x^61*y - x^60*y*z0 - x^60*z0^2 - x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^58*y + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 + x^57 - x^55*y*z0 + x^56 - x^55*y + x^45*y*z0^2,
 -x^115 + x^113*z0^2 - x^114 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^111 + x^110*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y - x^108*z0 - x^107*y*z0 - x^107*y + x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^106*y + x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^87*y*z0^2 - x^89 + x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^84*y*z0 + x^83*y*z0^2 - x^84*y + x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^82*y + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^80 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*z0^2 + x^71*y - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^69 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 - x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 + x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 - x^65*y + x^65*z0 + x^64*y*z0 - x^64*y + x^63*y*z0 + x^63*z0^2 + x^63*z0 + x^62*y*z0 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 - x^59*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^56*y*z0^2 - x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^55*y*z0 - x^55*y + x^46,
 x^115 - x^113*z0^2 - x^114 - x^113*z0 - x^112*z0^2 - x^112*y - x^112*z0 + x^110*y*z0^2 + x^111*y + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^109*z0 - x^107*y*z0^2 - x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y + x^105*z0 - x^104*z0^2 - x^104*y - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^102*z0 - x^100*y*z0^2 + x^101*y + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 + x^99*y*z0 - x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^98*y - x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 + x^95*y - x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*y - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 + x^90 + x^89*y - x^88*y*z0 - x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^84 - x^83*y - x^82*z0^2 + x^82*y - x^82*z0 - x^81*y*z0 + x^80*y*z0^2 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y - x^77*y*z0 - x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*z0^2 + x^70*y*z0^2 - x^71*y - x^71*z0 + x^70*y*z0 - x^69*y*z0^2 + x^70*y - x^70*z0 - x^68*y*z0^2 - x^70 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 + x^67*z0^2 + x^66*y*z0^2 + x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^65*y*z0 - x^65*z0^2 - x^66 + x^65*y + x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^63*y*z0 + x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 - x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^62 + x^61*y - x^61*z0 - x^60*y*z0 - x^61 + x^59*y*z0 - x^59*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*z0^2 - x^57*y*z0^2 + x^58*y - x^58*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56 + x^46*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^110*y - x^110*z0 + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 + x^103*z0 + x^102*y*z0 + x^103 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^100*z0^2 + x^99*y*z0^2 - x^100*y + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*y*z0 + x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y - x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^95*y + x^95*z0 - x^94*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 + x^91*y*z0 + x^92 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^89*y*z0 - x^89*z0^2 - x^89*y + x^89*z0 + x^88*z0^2 + x^88*y + x^88*z0 - x^87*y*z0 + x^87*z0^2 - x^88 - x^86*y*z0 + x^86*z0^2 - x^86*y + x^86*z0 - x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 - x^84*y + x^84*z0 - x^84 - x^83*y + x^82*y*z0 + x^83 - x^82*y + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^77 + x^76*y + x^75*y*z0 - x^74*y*z0^2 - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*z0 - x^73*y*z0 + x^72*y*z0^2 + x^74 - x^73*z0 - x^72*z0^2 + x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*z0 - x^70*z0^2 - x^70*y - x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^67 + x^66*z0 + x^65*z0^2 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*z0^2 - x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y + x^59*y*z0 - x^58*y*z0^2 - x^60 + x^57*y*z0^2 - x^58*y + x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 + x^56*y*z0 + x^55*y*z0^2 - x^57 - x^56*y + x^55*y + x^46*z0^2,
 -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^112 + x^111*z0 - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^110*y - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^107*y*z0^2 - x^109 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^106*z0^2 + x^105*y*z0^2 - x^106*y - x^106*z0 + x^105*z0^2 + x^104*y*z0^2 - x^105*y + x^104*y*z0 - x^103*y*z0^2 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^103 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*y*z0 + x^101 + x^100*z0 - x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 - x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^97*y - x^96*y*z0 + x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^96 + x^95*z0 + x^94*y*z0 - x^93*y*z0^2 + x^95 + x^94*y - x^93*y*z0 - x^92*y*z0^2 + x^93*y + x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 + x^92 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 - x^88*y + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^88 + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 - x^82 + x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^81 + x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^78 - x^77*z0 + x^76*y*z0 - x^75*y*z0^2 - x^76*z0 - x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*z0 - x^74*y*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 - x^71*y - x^70*y*z0 + x^70*z0^2 + x^71 + x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y - x^67*y*z0^2 - x^69 - x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^65*z0^2 + x^64*y*z0^2 + x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 - x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^61*y + x^60*y*z0 + x^60*z0^2 + x^61 - x^60*y + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^60 + x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^58*y + x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^46*y,
 -x^115 - x^114*z0 + x^113*z0 + x^112*z0^2 + x^112*y + x^111*y*z0 + x^111*z0^2 + x^112 - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 - x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 + x^107*y*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^107*y + x^107*z0 + x^106*y*z0 - x^107 - x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^106 + x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^104*z0 - x^102*y*z0^2 + x^103*y - x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^102*y - x^101*y - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^99*y*z0 + x^98*y*z0^2 + x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^99 - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*y - x^96*z0^2 + x^95*y*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 + x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 + x^95 + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*y - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*y - x^83 - x^82*y - x^81*y*z0 + x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^78 + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^77 + x^75*y + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^72*y*z0^2 + x^74 - x^73*y + x^73*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 + x^70*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^69*y - x^69*z0 - x^68*z0^2 + x^69 - x^68*z0 + x^67*y*z0 + x^68 - x^67*y - x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^62 - x^61*z0 + x^60*y*z0 + x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*z0^2 - x^59 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*y + x^55*y*z0 - x^56 + x^55*y + x^46*y*z0,
 -x^114*z0 - x^113*z0^2 - x^114 + x^112*z0^2 + x^113 + x^112*z0 + x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*y + x^111*z0 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^108*y - x^108*z0 - x^108 - x^107*y + x^107*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^106 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y + x^104*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^100*y*z0 - x^99*y*z0^2 - x^100*y - x^100*z0 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*y + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^94*z0^2 - x^94*y - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^92*y*z0 + x^91*y*z0^2 + x^93 + x^92*y + x^92*z0 + x^91*y*z0 + x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^89*y - x^89*z0 + x^88*z0^2 - x^89 - x^88*y - x^88*z0 - x^86*y*z0^2 + x^88 - x^87*z0 + x^86*z0^2 + x^87 + x^86*y - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^85 + x^83*y*z0 + x^82*y*z0^2 - x^84 + x^83*y - x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^80 - x^79*y - x^79*z0 - x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*z0 + x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y + x^75*z0 + x^74*y*z0 - x^75 + x^74*y - x^74*z0 - x^73*y*z0 - x^73*y - x^73*z0 - x^72*z0^2 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^71*y + x^69*y*z0^2 + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y + x^66*z0 - x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 + x^64*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*z0^2 - x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 + x^57*z0^2 - x^57*z0 - x^56*z0^2 + x^55*y*z0^2 - x^56*z0 + x^55*y*z0 - x^56 - x^55*y + x^46*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 + x^112*z0^2 + x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^110 + x^109*y - x^109*z0 - x^108*y*z0 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y + x^105*z0^2 + x^106 - x^105*z0 - x^104*z0^2 + x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 - x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^103 - x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^98*y*z0^2 + x^100 + x^99*z0 - x^99 - x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y - x^97*z0 - x^96*z0^2 - x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^92*y*z0^2 - x^94 + x^93*y + x^92*z0^2 - x^93 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^90 + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 - x^88*y + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 - x^87*y + x^86*y*z0 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^86 + x^85*y + x^85*z0 - x^83*y*z0^2 + x^85 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^83*z0 + x^82*y*z0 - x^82*z0^2 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0 + x^80*z0^2 - x^81 + x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^76*y*z0^2 - x^78 - x^76*y*z0 + x^76*z0^2 + x^77 + x^76*y - x^76*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 + x^73 - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^69*z0^2 + x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 + x^68 + x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 - x^65*y + x^65*z0 + x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 + x^62*y*z0^2 + x^63*y + x^63*z0 + x^62*y*z0 + x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*y - x^61*z0 - x^60*y + x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^55*y + x^47,
 x^114 + x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 + x^112 - x^111*y - x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^109*y - x^108*z0^2 - x^107*y*z0^2 + x^108*y - x^108*z0 - x^107*y*z0 - x^106*y*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 + x^105 - x^104*y + x^103*y*z0 - x^103*z0^2 - x^103*z0 + x^102*y*z0 - x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^98*y*z0 - x^98*z0^2 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 + x^95*y - x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 - x^94 + x^93*y + x^93*z0 + x^92*z0^2 - x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*z0 - x^90*z0^2 + x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^89*y + x^88*y*z0 + x^87*y*z0^2 - x^88*y - x^88*z0 + x^87*y*z0 + x^88 + x^87*y - x^86*y*z0 - x^86*z0^2 - x^87 - x^85*y*z0 + x^85*z0^2 + x^86 + x^85*y + x^85*z0 - x^84*y*z0 - x^83*y*z0^2 - x^84*y - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 - x^83*y + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^78*y*z0^2 - x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*y + x^77*z0^2 - x^77*y - x^77*z0 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 - x^75*y + x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^72 + x^71*y - x^71*z0 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 + x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 - x^67*y*z0^2 + x^69 + x^68*y - x^68*z0 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^64*z0^2 - x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*y + x^63*z0 - x^61*y*z0^2 - x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^60*y*z0 + x^61 - x^60*y + x^60*z0 + x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y + x^58*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y + x^56*y*z0 - x^55*y*z0^2 - x^56*y - x^55*y*z0 + x^47*z0,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^111*z0 + x^110*y*z0 - x^111 + x^109*y*z0 + x^109*z0^2 + x^110 + x^108*y*z0 + x^108*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^106*y*z0 + x^106*y - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 + x^105*y - x^104*y*z0 - x^104*z0^2 - x^105 + x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 + x^102*y - x^101*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*y - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*z0 + x^95*y*z0 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^93*y*z0 + x^94 + x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 - x^91*z0^2 - x^90*y*z0 + x^89*y*z0^2 - x^91 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*y + x^88*y*z0 + x^87*y*z0^2 + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^85*y*z0 - x^85*y + x^83*y*z0^2 + x^84*z0 + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y + x^80*z0 + x^79*z0^2 + x^80 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^79 + x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 - x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^75 + x^74*y + x^74*z0 - x^73*y*z0 - x^74 - x^73*y + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y + x^68*y*z0 + x^68*z0^2 + x^68*y - x^68*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 - x^67 - x^66*z0 - x^64*y*z0^2 - x^65*y + x^64*y*z0 + x^65 + x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^63*z0 + x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^58*z0^2 + x^57*y*z0^2 - x^59 + x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^56*y*z0 - x^56*y - x^56*z0 - x^55*y + x^47*z0^2,
 -x^115 - x^114*z0 - x^114 - x^112*z0^2 + x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^112 + x^111*y - x^110*z0^2 + x^109*y*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*z0^2 + x^107*y*z0^2 - x^108*y - x^108*z0 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^105*y*z0^2 - x^107 - x^106*y - x^105*y*z0 + x^104*y*z0^2 - x^105*y + x^104*z0^2 + x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^101*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*z0^2 - x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 - x^92*z0^2 + x^92*z0 - x^90*y*z0^2 + x^92 - x^91*y - x^91*z0 - x^90*z0^2 + x^91 - x^90*y - x^89*y*z0 - x^89*z0^2 + x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^88*z0 - x^87*y*z0 - x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^83*y*z0 - x^82*y*z0^2 - x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 + x^81*y + x^81*z0 - x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^76*y*z0^2 - x^77*y + x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^74*y*z0^2 - x^76 + x^75*y + x^74*y*z0 - x^73*y*z0^2 - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 - x^73*y + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^73 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 - x^69*y*z0^2 + x^71 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 - x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 - x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 + x^65 + x^64*y - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y - x^63*z0 + x^62*z0^2 + x^63 + x^62*y - x^62*z0 - x^60*y*z0^2 + x^61*z0 - x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0^2 - x^57 - x^56*y + x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^47*y,
 x^114*z0 + x^113*z0^2 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*z0 + x^110*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^110 + x^109*y + x^109*z0 - x^108*y*z0 - x^107*y*z0^2 + x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y - x^107*z0 + x^106*y*z0 - x^105*y*z0^2 - x^107 - x^105*y*z0 + x^106 - x^104*y*z0 - x^105 - x^104*y - x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*y*z0 + x^103 + x^102*y + x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 - x^97*y*z0 - x^98 - x^97*y + x^97*z0 - x^96*y*z0 + x^95*y*z0^2 - x^96*z0 - x^95*z0^2 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*y - x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^92 + x^90*y*z0 + x^90*y - x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 - x^86*z0 - x^85*y*z0 - x^84*y*z0^2 - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*y - x^82*y*z0 + x^81*y*z0^2 - x^83 + x^82*z0 - x^81*y*z0 - x^80*y*z0 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 + x^76 - x^75*y - x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^71*y - x^71*z0 + x^70*z0^2 - x^69*y*z0^2 - x^70*y + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^69 - x^67*z0^2 + x^66*y*z0^2 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^65*y*z0 - x^64*y*z0^2 - x^66 + x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 - x^65 + x^64*y + x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^60*y*z0^2 - x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*y*z0 + x^57 + x^56*z0 + x^47*y*z0,
 -x^113 - x^112*z0 + x^111*z0^2 + x^112 - x^111*z0 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*y + x^108*y*z0 + x^108*z0^2 + x^109 + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 - x^103*z0^2 + x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^100*y*z0^2 + x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^99*z0 - x^98*y*z0 + x^97*y*z0^2 - x^98*y - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*y*z0 + x^94 + x^93*y - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*y - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 - x^84*y*z0^2 - x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^83*y*z0 + x^83*z0^2 - x^84 + x^83*y + x^83*z0 + x^83 + x^82*y - x^81*y*z0 - x^81*y + x^81*z0 - x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^78*y*z0^2 + x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*z0 + x^76*y*z0^2 - x^77*y - x^76*y - x^75*y*z0 - x^74*y*z0^2 + x^75*y - x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 + x^72*y*z0^2 + x^74 + x^73*y + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^71*z0^2 + x^70*y*z0^2 + x^72 - x^71*y - x^71*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y - x^70*z0 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^67*y - x^67*z0 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 - x^63*y*z0^2 - x^65 - x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y - x^62*z0^2 - x^63 + x^62*y + x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0 - x^60*z0^2 - x^60*y - x^60*z0 + x^58*y*z0^2 + x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 + x^59 + x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y + x^57*z0 - x^56*z0^2 + x^57 - x^56*y - x^56*z0 - x^56 + x^47*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 - x^114 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^112 + x^111*y - x^111*z0 + x^110*z0^2 + x^111 + x^109*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^106*y*z0^2 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 - x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^105*y - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^102*y - x^102*z0 - x^101*z0^2 - x^102 + x^101*y + x^101 + x^100*y - x^99*z0^2 - x^99*y - x^98*y*z0 + x^97*y*z0^2 + x^98*z0 - x^97*y*z0 + x^96*y*z0^2 - x^98 + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 - x^96*y - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*z0 + x^92*y*z0 - x^91*y*z0^2 + x^93 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 + x^91 + x^90*z0 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^84*y - x^84*z0 - x^83*z0^2 + x^83*z0 + x^82*y*z0 - x^82*y + x^81*y*z0 - x^81*z0^2 + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^80*z0 + x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^77*z0^2 + x^76*y*z0^2 + x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^74 - x^73*y + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^70 + x^69*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 + x^67*y - x^66*z0^2 + x^65*y*z0^2 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^66 - x^65*y - x^65*z0 - x^64*y*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^62*y*z0 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^61 + x^60*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^58*y*z0 + x^57*y*z0^2 + x^59 - x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^58 - x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^56*y - x^56*z0 + x^55*y*z0 - x^55*y + x^48,
 x^115 + x^114*z0 - x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 - x^112 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^105*y*z0 + x^105*z0^2 + x^106 + x^105*y + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^104 + x^103*y - x^102*y*z0 + x^102*z0^2 - x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 + x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 - x^92*y*z0 - x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*z0 - x^87*y*z0 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^87 - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 + x^86 + x^85*y + x^84*y*z0 - x^84*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^84 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 - x^83 - x^82*y + x^81*y*z0 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 + x^80*y - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^80 - x^79*y + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 + x^74*y*z0^2 + x^75*y + x^75*z0 + x^75 - x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*z0 - x^70 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^68*y + x^68*z0 - x^67*y*z0 + x^68 - x^66*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*z0^2 - x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^64 + x^63*y - x^63*z0 + x^62*y*z0 + x^61*y*z0^2 + x^63 + x^62*y + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^60*y*z0 - x^60*z0^2 + x^61 - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*z0 + x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 + x^58 - x^57*z0 - x^56*y*z0 - x^57 - x^56*y - x^55*y*z0 - x^55*y + x^48*z0,
 -x^115 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 + x^112*y - x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 - x^108*y*z0^2 - x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^108*y - x^107*y*z0 - x^107*z0^2 - x^108 - x^107*y + x^106*y*z0 + x^105*y*z0^2 - x^107 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^104*y*z0 - x^105 - x^104*y - x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103*z0 + x^102*z0^2 - x^103 + x^100*y*z0^2 - x^102 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^98*y*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^97*z0^2 + x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^95*z0^2 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*y + x^94*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y - x^92*y*z0 + x^91*z0^2 - x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 + x^86*y*z0^2 - x^87*y - x^87*z0 - x^86*y*z0 + x^87 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^85 + x^84*z0 - x^83*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 - x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y + x^78*y*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^76*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^73*y + x^73*z0 + x^71*y*z0^2 - x^72*y + x^71*y*z0 + x^70*y*z0^2 - x^72 - x^70*y*z0 + x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*z0 - x^67*y*z0^2 - x^69 + x^68*y - x^67*z0^2 + x^66*y*z0^2 - x^68 + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^65 + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^63 + x^62*y - x^61*z0^2 + x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^60*y + x^60*z0 + x^60 + x^59*y - x^59*z0 + x^57*y*z0^2 - x^59 + x^56*y*z0^2 - x^58 + x^56*z0^2 + x^55*y*z0^2 - x^56 + x^48*z0^2,
 -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*y + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 - x^109 + x^108*y + x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 - x^105*y*z0^2 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^104*y + x^104*z0 - x^103*z0^2 - x^103*y + x^102*z0^2 + x^103 + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 - x^98*y*z0 - x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^98 - x^97*y + x^97*z0 - x^97 - x^96*y - x^94*y*z0^2 - x^96 + x^95*y + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 - x^94 - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 + x^92*z0 + x^91*y*z0 + x^91*y - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 - x^88*y + x^88*z0 + x^87*y*z0 + x^88 + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y - x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*z0 + x^84*y*z0 - x^84*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 - x^82*y*z0^2 - x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^83 - x^82*z0 - x^80*y*z0^2 + x^80*y*z0 - x^79*y*z0^2 - x^81 - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^78*y + x^77*y*z0 - x^76*y*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^75*y*z0 + x^75*z0^2 + x^76 + x^75*y + x^75*z0 - x^73*y*z0^2 - x^75 + x^74*y - x^73*z0^2 + x^72*y*z0^2 - x^71*y*z0^2 + x^72*y + x^72*z0 + x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*z0^2 - x^68*y*z0^2 - x^70 + x^69*z0 + x^68*y*z0 + x^68*z0^2 + x^69 - x^68*y + x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 - x^65*y*z0^2 + x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 + x^65*y - x^65*z0 - x^64*y*z0 + x^63*y*z0^2 - x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*z0 + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 - x^59*z0 + x^57*y*z0^2 + x^59 - x^58*y + x^58 - x^57*y - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^55*y*z0 - x^56 - x^55*y + x^48*y,
 -x^114*z0 - x^113*z0^2 - x^113*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 + x^110*y*z0 + x^110*z0^2 + x^111 - x^110*z0 - x^109*z0^2 - x^110 - x^109*y - x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^105*y*z0 + x^105*z0^2 + x^105*y - x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*y + x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 - x^99*y*z0 - x^99*z0^2 - x^100 - x^98*y*z0 - x^97*y*z0^2 - x^99 + x^98*y + x^98*z0 - x^96*y*z0^2 + x^97*y - x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^94*y - x^93*z0^2 + x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*z0^2 - x^93 + x^92*y + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 + x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*z0^2 - x^87 - x^86*y + x^86*z0 + x^85*y*z0 - x^86 - x^85*y + x^85*z0 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*y - x^83 + x^82*y + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^82 - x^80*z0^2 - x^79*y*z0^2 + x^80*z0 - x^79*y*z0 - x^79*z0^2 - x^79*y + x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 - x^78 + x^77*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 - x^75*z0^2 - x^76 - x^75*z0 + x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y + x^73*y*z0 + x^74 - x^73*z0 - x^71*y*z0^2 - x^73 + x^71*y*z0 - x^70*y*z0^2 + x^72 + x^69*y*z0^2 - x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*y - x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 + x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 + x^64*y - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*y*z0 + x^63 - x^62*y + x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^58*y*z0 + x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 + x^55*y*z0^2 + x^55*y*z0 - x^56 - x^55*y + x^48*y*z0,
 -x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 - x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^105*y - x^104*z0^2 + x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^101*y*z0 + x^101*z0^2 + x^101*y - x^101*z0 + x^100*y*z0 - x^99*y*z0^2 - x^101 - x^100*y + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y + x^98*y*z0 + x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^97 - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y - x^94*y*z0 - x^94*y - x^94*z0 + x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^93 - x^92*y + x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^92 + x^91*y + x^91*z0 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^88*y*z0 + x^88*z0^2 + x^89 + x^88*y - x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 - x^87*y - x^86*y*z0 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^82*y - x^81*y*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^79*y*z0^2 - x^81 + x^80*z0 - x^79*z0^2 - x^80 - x^79*y + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y + x^76*y*z0^2 + x^77*y + x^77*z0 + x^75*y*z0^2 - x^77 - x^76*z0 + x^76 + x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^74*y - x^74*z0 + x^73*y*z0 - x^72*y*z0^2 - x^74 - x^72*y*z0 - x^73 + x^72*z0 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 - x^70*y - x^70*z0 + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^69 + x^67*y*z0 - x^66*y*z0^2 - x^68 - x^67*y - x^67*z0 - x^65*y*z0^2 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y - x^64*y*z0 + x^65 - x^64*y - x^64*z0 - x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y + x^59*z0 - x^57*y*z0^2 - x^58*y + x^57*y*z0 + x^57*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 + x^56 + x^48*y*z0^2,
 x^114*z0 + x^113*z0^2 - x^113*z0 - x^113 - x^112*z0 - x^111*y*z0 - x^110*y*z0^2 + x^112 - x^111*z0 + x^110*y*z0 + x^111 + x^110*y + x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^110 - x^109*y - x^109*z0 + x^108*y*z0 + x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*y + x^107*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 - x^105*y*z0 + x^106 - x^105*y - x^105*z0 + x^104*y*z0 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*z0 + x^102*y*z0 - x^101*y*z0^2 + x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 - x^100 + x^99*y - x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^91*z0^2 - x^90*y*z0^2 - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^90 + x^89*z0 + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*z0 - x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*z0^2 + x^83*y*z0^2 + x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^81*y*z0^2 + x^83 + x^82*z0 - x^80*y*z0^2 - x^81*y - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^79*y*z0^2 + x^81 - x^80*z0 - x^79*y*z0 - x^78*y*z0^2 + x^80 - x^79*y - x^78*y*z0 - x^78*y - x^78*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^76 - x^75*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^74 - x^73*z0 + x^72*z0^2 + x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^72 + x^71*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y + x^68*y*z0 + x^68*y + x^68*z0 - x^67*y*z0 - x^66*y*z0^2 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^66 + x^65 + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 + x^62*y*z0 + x^63 - x^62*z0 + x^61*z0^2 + x^62 - x^61*y - x^60*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 - x^59 - x^58*y + x^58 + x^57*y + x^57*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 + x^56 + x^55*y + x^49,
 -x^114*z0 - x^113*z0^2 + x^114 - x^112*z0 + x^111*y*z0 + x^110*y*z0^2 + x^112 - x^111*y - x^111*z0 - x^110*z0^2 + x^111 + x^109*y*z0 + x^109*z0^2 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 + x^106*z0^2 + x^107 + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 + x^106 - x^105*y - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*z0 + x^102*y*z0 + x^101*y*z0^2 + x^103 - x^102*y + x^102*z0 - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0 - x^100 + x^99*z0 - x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*z0 - x^95*y*z0^2 - x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^96 - x^95*y + x^95*z0 - x^94*y + x^94*z0 + x^93*y*z0 - x^93*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y - x^91*z0 - x^89*y*z0^2 - x^90*y + x^89*z0^2 - x^88*y*z0^2 + x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*z0 + x^86*y*z0 - x^85*y*z0^2 + x^86*y + x^86*z0 - x^84*y*z0^2 + x^86 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y - x^84*z0 - x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^83 - x^82*y - x^82*z0 + x^81*z0^2 + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^77*z0 + x^76*y*z0 + x^77 + x^76*z0 + x^75*y*z0 - x^76 - x^75*z0 - x^74*z0^2 + x^75 + x^73*y*z0 - x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^71 - x^70*y + x^70*z0 + x^68*y*z0^2 - x^70 + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 - x^68*y + x^67*y*z0 - x^66*y*z0^2 - x^67*y - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 - x^67 - x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*z0 - x^63*y*z0^2 - x^65 + x^64*y - x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^62*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^61 - x^60*y - x^59*z0^2 + x^58*y*z0^2 + x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 - x^55*y*z0 - x^56 + x^49*z0,
 x^115 + x^114*z0 + x^114 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y - x^111*y*z0 - x^112 - x^111*y - x^110*y*z0 + x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y - x^109*z0^2 + x^110 + x^109*y + x^109*z0 - x^107*y*z0^2 - x^108*y - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^108 + x^107*y - x^107*z0 + x^106*y*z0 - x^106*z0^2 + x^107 + x^106*y - x^105*y*z0 - x^105*z0^2 + x^105*y - x^105*z0 + x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*z0^2 + x^101 - x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^99*y - x^98*z0^2 + x^99 + x^98*y - x^98*z0 - x^97*y*z0 + x^96*y*z0^2 + x^98 - x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^96*z0 - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 - x^96 - x^94*y*z0 + x^93*y*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 + x^94 - x^93*y - x^93*z0 - x^92*y*z0 - x^91*y*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0 + x^90*y*z0 - x^90*z0^2 + x^91 + x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 + x^90 - x^89*y - x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*y - x^86*y*z0 - x^86*z0^2 + x^86*y - x^86 + x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^85 - x^84*z0 + x^83*z0^2 - x^84 - x^83*y + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^81*y - x^80*y*z0 - x^80*y - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^79*z0 + x^78*z0^2 + x^79 + x^78*y - x^77*y*z0 + x^77*z0^2 - x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^76*y - x^75*y*z0 + x^74*y*z0^2 + x^76 + x^75*y - x^75*z0 + x^74*z0^2 + x^75 - x^74*y - x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71 + x^70*y + x^70*z0 - x^69*z0^2 + x^68*y*z0^2 - x^70 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^67 + x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^63*y*z0^2 - x^64*y + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y - x^63 - x^62*y - x^61*y*z0 + x^61*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y + x^59*y*z0 - x^59*z0^2 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 - x^57*y - x^57*z0 - x^56*z0^2 - x^55*y*z0^2 + x^57 - x^56*z0 + x^55*y*z0 - x^56 + x^49*z0^2,
 x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*y + x^109*z0 - x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 - x^106 - x^105*y - x^105*z0 + x^104*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*z0^2 - x^100 + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^98*y - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^97 + x^96*y + x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*z0 + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*z0 + x^92*y*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 + x^90*z0 - x^89*y*z0 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^85*y*z0 + x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 + x^84*y + x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*z0^2 + x^81*y - x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 - x^79*y - x^78*y*z0 - x^77*y*z0^2 + x^79 + x^78*y - x^76*y*z0^2 - x^78 + x^77*y + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 + x^75*z0^2 + x^74*y*z0^2 - x^75*y - x^73*y*z0^2 + x^74*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 + x^73*z0 + x^72*z0^2 + x^72*y - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^68*y - x^68*z0 - x^66*y*z0^2 - x^68 + x^67*y - x^67*z0 + x^66*z0^2 - x^67 - x^66*y - x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*y + x^64*z0^2 - x^63*y*z0^2 - x^64*y + x^63*y*z0 + x^62*y*z0^2 - x^64 + x^62*z0^2 - x^63 - x^62*y + x^62*z0 + x^61*z0^2 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 + x^59 - x^58*y + x^58*z0 + x^57*y*z0 - x^58 - x^56*y*z0 - x^56*y + x^55*y*z0 - x^55*y + x^49*y,
 x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 + x^112*z0^2 - x^113 - x^112*y + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*y*z0 - x^109*y*z0^2 + x^110*y - x^109*z0^2 - x^108*y*z0^2 - x^109*y - x^108*y*z0 - x^108*z0^2 + x^109 + x^108*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 + x^106*y*z0 - x^106*z0^2 - x^107 + x^106*y - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^104*z0 + x^103*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^101*y*z0 + x^100*y*z0^2 + x^100*z0^2 - x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^99*z0 + x^98*z0^2 + x^97*y*z0^2 + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^98 + x^96*y*z0 + x^95*y*z0^2 - x^96*y - x^96*z0 - x^94*y*z0^2 - x^95*y - x^95*z0 + x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^94 - x^93*y - x^92*y*z0 - x^93 + x^92*y - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^91*y + x^91*z0 + x^90*y*z0 + x^89*y*z0^2 + x^91 + x^90*z0 - x^89*z0^2 + x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^88*y + x^88*z0 - x^87*z0^2 - x^87*y - x^87*z0 + x^86*z0^2 + x^87 - x^86*y - x^86*z0 + x^86 + x^85*y - x^84*y*z0 - x^84*z0^2 - x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*y*z0 + x^84 + x^83*y - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y + x^81*y*z0 - x^81*z0^2 - x^82 + x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^79*y*z0 - x^79*z0^2 + x^80 - x^79*y - x^78*y*z0 - x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^77*y + x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 - x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^74*y + x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 + x^72*z0^2 + x^73 - x^72*y + x^70*y*z0^2 - x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^69*y*z0 + x^69*z0^2 + x^70 - x^69*z0 - x^68*y*z0 + x^69 + x^68*z0 - x^67*y*z0 - x^68 + x^67*y + x^66*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 + x^64*y + x^64*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*z0 + x^60*y*z0^2 - x^61*y + x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^60*y + x^60*z0 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 + x^59*y + x^58*z0^2 + x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56*z0 + x^55*y*z0 - x^55*y + x^49*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 - x^110*y + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y + x^108*z0 - x^108 - x^107*y + x^107*z0 - x^105*y*z0^2 - x^106*y - x^105*y*z0 - x^105*z0^2 + x^106 - x^105*y + x^105*z0 + x^104*z0^2 - x^105 + x^104*y - x^103*y*z0 - x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^101 + x^100*z0 + x^99*y*z0 - x^99*z0^2 - x^98*y*z0^2 + x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^97 - x^96*y - x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*y + x^95*z0 + x^94*y*z0 - x^94*z0^2 - x^95 - x^94*z0 + x^92*y*z0^2 + x^94 - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^92*y + x^92*z0 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^89*y + x^89*z0 - x^88*y*z0 - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^86*y*z0^2 + x^88 - x^87*y + x^87*z0 + x^86*z0^2 + x^87 + x^85*y*z0 - x^84*y*z0^2 - x^86 + x^84*y*z0 - x^84*z0^2 - x^84*z0 - x^83*y*z0 - x^82*y*z0^2 + x^83*y + x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y + x^79*y*z0 - x^80 + x^79*z0 + x^77*y*z0^2 - x^79 - x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^77*z0 + x^76*y*z0 + x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^75*z0^2 + x^75*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^72*y*z0^2 - x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^73 - x^72*z0 + x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 + x^71*y + x^70*y*z0 + x^70*z0^2 - x^70*z0 + x^69*z0 - x^68*y*z0 - x^67*y*z0^2 - x^69 + x^68*z0 + x^67*z0^2 - x^65*y*z0^2 + x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^64*z0 + x^62*y*z0^2 + x^64 - x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 + x^62*y + x^61*y*z0 + x^61*z0^2 + x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 - x^58*y*z0^2 + x^60 + x^59*y + x^58*y*z0 - x^58*z0^2 - x^59 - x^58*z0 - x^57*z0^2 + x^58 + x^57*z0 - x^56*y*z0 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^55*y + x^49*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y - x^110*y + x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*z0 + x^108*z0^2 - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^106*z0^2 + x^107 + x^106*z0 - x^104*y*z0^2 - x^106 - x^105*y + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y - x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*z0^2 + x^101*y*z0^2 + x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^99*y*z0^2 + x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^99*y + x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 - x^97*y - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y - x^96*z0 - x^96 - x^95*y - x^95*z0 + x^94*y*z0 + x^95 - x^93*z0^2 + x^94 + x^93*z0 + x^91*y*z0^2 - x^93 - x^92*y + x^91*y*z0 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^90*y + x^89*y*z0 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*z0 - x^87*y*z0 - x^87*z0^2 + x^88 + x^87*y - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^85*y*z0 - x^84*y*z0^2 + x^86 + x^85*y + x^85*z0 + x^84*y*z0 - x^84*z0^2 + x^84*y + x^84*z0 + x^83*y*z0 - x^83*z0^2 + x^84 + x^83*y + x^83*z0 - x^82*z0^2 - x^83 + x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*y + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*z0 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^79*z0 - x^78*y*z0 + x^79 + x^77*y*z0 + x^76*y*z0^2 + x^78 - x^76*y*z0 + x^76*z0^2 + x^77 + x^76*y + x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*z0 - x^74*y*z0 + x^73*y*z0^2 - x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^72*y + x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 + x^71*y - x^71*z0 + x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^70 + x^69*y + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^69 - x^68*z0 - x^66*y*z0^2 - x^68 + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^65*y*z0 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^56*y - x^56*z0 - x^55*y*z0 + x^55*y + x^50,
 x^114*z0 + x^113*z0^2 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^111 - x^110*y - x^110*z0 - x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*z0^2 + x^109 + x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^107 + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y - x^104*z0 - x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*y + x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^102 - x^101*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 + x^98*y + x^98*z0 + x^97*y*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*z0^2 - x^93*z0 - x^92*z0^2 + x^91*y*z0^2 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 - x^90 - x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*y + x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y + x^84*y*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^84 - x^81*y*z0^2 - x^83 - x^82*z0 + x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^80*z0^2 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y - x^78*y*z0 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*y*z0 - x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*y - x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^75*y + x^74*y*z0 - x^75 + x^73*y*z0 - x^72*y*z0^2 - x^74 + x^73*y - x^72*y*z0 - x^72*z0^2 - x^72*y - x^71*z0^2 + x^72 + x^71*y - x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 - x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y + x^69*z0 + x^68*y*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 - x^68*y + x^67*z0^2 + x^67*y + x^67*z0 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 + x^64*y*z0^2 - x^66 + x^65*z0 - x^64*y*z0 - x^63*y*z0^2 + x^65 + x^64*z0 - x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*z0 - x^62*y*z0 - x^63 + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^60*y*z0 + x^61 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^57*y + x^57*z0 - x^56*y*z0 - x^56*z0^2 - x^57 + x^56*z0 - x^56 + x^50*z0,
 x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^112 + x^111*y - x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*z0 - x^109*y*z0 - x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 - x^108*z0^2 + x^108*y - x^107*y*z0 - x^107*z0^2 + x^108 + x^105*y*z0^2 + x^107 + x^105*y*z0 - x^104*y*z0^2 + x^106 + x^104*y*z0 + x^104*y - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y + x^103*z0 - x^102*y*z0 - x^102*y - x^101*z0^2 + x^102 + x^101*z0 + x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*y + x^99*z0^2 - x^98*y*z0^2 + x^99*z0 - x^98*y*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 + x^97*y + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^94*y*z0^2 - x^95*y + x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y - x^92*z0^2 + x^93 + x^92*y + x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y + x^90*z0 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 - x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 + x^88 + x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 + x^85*z0^2 - x^84*y*z0^2 + x^85*y + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*y - x^84*z0 - x^83*z0^2 + x^83*y + x^83*z0 + x^82*z0^2 - x^83 + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^80*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 - x^78 + x^77*y - x^77*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*z0 - x^75*y*z0 - x^76 + x^75*z0 - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^73 - x^72*z0 + x^70*y*z0^2 + x^72 + x^71*y - x^71*z0 + x^70*y*z0 - x^70*z0^2 - x^69*y*z0 + x^68*y*z0^2 - x^70 + x^69*y + x^68*y*z0 + x^67*y*z0^2 + x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^65 + x^63*z0^2 - x^62*y*z0^2 - x^64 + x^63*y + x^63*z0 - x^62*z0^2 + x^61*y*z0^2 - x^63 - x^62*y + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 - x^61*z0 + x^60*z0^2 - x^59*y*z0^2 + x^61 + x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 + x^59*y + x^59*z0 + x^58*z0^2 + x^58*z0 + x^57*y*z0 + x^57*z0^2 - x^56*y*z0^2 - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y + x^56*z0 + x^55*y*z0 + x^56 + x^55*y + x^50*z0^2,
 -x^115 + x^113*z0^2 + x^112*z0^2 + x^112*y - x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*z0 - x^110*z0^2 - x^109*y*z0^2 - x^111 + x^110*z0 + x^109*y*z0 + x^108*y*z0^2 + x^110 - x^109*y - x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 + x^108 + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 - x^105*z0^2 - x^106 - x^105*y + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^104 + x^103*y + x^103 + x^102*y + x^101*z0^2 - x^100*y*z0^2 + x^102 - x^101*z0 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 + x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^97*z0 - x^95*y*z0^2 + x^97 + x^96*y - x^96*z0 + x^95*y*z0 + x^95*z0^2 - x^95*y - x^95*z0 - x^94*z0^2 - x^95 + x^93*y*z0 + x^94 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y - x^91*z0 - x^90*z0^2 + x^90*y + x^90*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 - x^89*z0 + x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^87*z0 + x^86*z0 + x^85*y*z0 + x^84*y*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 + x^83*y*z0^2 - x^85 - x^84*y - x^83*y*z0 - x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 - x^82*z0^2 + x^82*z0 - x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 + x^81 - x^80*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^79*z0 + x^77*y*z0^2 - x^79 + x^78*y + x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 + x^74*y*z0^2 - x^76 + x^75*z0 + x^74*y*z0 - x^73*y*z0^2 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y + x^72*z0 + x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 + x^69*y*z0 - x^69*y - x^68*z0^2 - x^69 - x^68*y + x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*z0 + x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 - x^64*z0^2 + x^63*y*z0^2 + x^64*y + x^63*z0^2 + x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 - x^62*y*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*z0^2 - x^59*y*z0^2 - x^61 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 + x^57*y*z0 - x^57*y + x^55*y*z0^2 + x^57 + x^56*y - x^56 + x^55*y + x^50*y,
 -x^114*z0 - x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 + x^111*y*z0 + x^110*y*z0^2 - x^111*y - x^110*y*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*y - x^109*y*z0 + x^109*z0^2 - x^110 + x^109*z0 + x^107*y*z0^2 + x^109 - x^108*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 + x^105*y*z0^2 + x^107 + x^106*y + x^106*z0 + x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^104*z0 + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^102*y*z0 + x^102*z0^2 + x^103 + x^102*y + x^102*z0 + x^101*y*z0 + x^101*z0^2 - x^100*y*z0^2 - x^102 - x^101*y - x^101*z0 + x^99*y*z0^2 + x^101 + x^100*y - x^100*z0 + x^99*y*z0 + x^98*y*z0^2 - x^100 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y + x^95*y*z0 + x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 + x^94*z0^2 - x^95 + x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 + x^93 + x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^91*y - x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^90 + x^89*y + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 - x^87*y + x^86*y*z0 + x^85*y*z0^2 + x^86*y - x^85*y*z0 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 + x^83*y*z0 - x^83*z0^2 - x^83*y - x^83*z0 + x^82*y*z0 + x^81*y*z0^2 + x^83 - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^80*y - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*y + x^79*z0 - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*z0 - x^75*z0^2 + x^76 + x^75*y + x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^72*y*z0^2 + x^74 - x^73*z0 - x^71*y*z0^2 + x^73 + x^72*y - x^71*y*z0 - x^71*z0^2 + x^72 + x^71*y + x^69*y*z0^2 - x^71 - x^70*y + x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^67 + x^66*y - x^66*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^64*z0^2 - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^64 + x^63*z0 - x^62*y*z0 + x^63 - x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*z0^2 - x^60*y - x^59*y*z0 + x^59*z0^2 + x^59*y + x^58*y*z0 - x^57*y*z0^2 + x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 + x^56*y - x^55*y*z0 - x^56 + x^50*y*z0,
 x^115 - x^114*z0 + x^113*z0^2 + x^113*z0 + x^112*z0^2 - x^112*y + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^112 - x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*z0 + x^109*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^107*y*z0^2 - x^109 - x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^107 - x^106*z0 - x^105*z0^2 + x^106 - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^103*y*z0^2 - x^104*y + x^103*y*z0 + x^103*z0^2 + x^104 - x^103*y + x^103*z0 + x^102*z0^2 - x^101*y*z0^2 + x^102*y + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*y + x^100*z0^2 + x^99*y*z0^2 + x^100*y + x^100*z0 - x^99*z0^2 - x^98*y*z0^2 + x^100 - x^99*y - x^99*z0 + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*z0 + x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^97 - x^95*z0^2 - x^94*y*z0^2 + x^96 + x^95*y + x^94*y*z0 - x^93*y*z0^2 - x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 - x^94 - x^93*y + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^92*z0 - x^92 - x^91*y - x^90*y*z0 - x^89*y*z0^2 + x^91 - x^90*y - x^90*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^87*z0^2 + x^86*y*z0^2 + x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 + x^85*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 - x^84*y - x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^81*z0 + x^79*y*z0^2 - x^80*y + x^80*z0 + x^78*y*z0^2 + x^79*y - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^76*y*z0^2 + x^78 - x^77*y - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 + x^77 - x^76*y + x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^75*y + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*z0 + x^70*y*z0^2 - x^71*y - x^71*z0 - x^70*y*z0 - x^71 - x^70*y - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66 - x^65*y + x^65*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^63*y*z0 - x^63*z0^2 + x^63*y - x^61*y*z0^2 - x^63 + x^62*y - x^62*z0 - x^61*z0^2 - x^60*y*z0^2 + x^61*y - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 + x^59*y - x^59*z0 - x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^57*z0^2 + x^57*y + x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^56*y + x^56*z0 - x^55*y*z0 - x^55*y + x^50*y*z0^2,
 -x^115 + x^113*z0^2 - x^112*z0^2 - x^113 + x^112*y + x^111*z0^2 - x^110*y*z0^2 + x^112 + x^109*y*z0^2 - x^111 + x^110*y - x^109*z0^2 - x^108*y*z0^2 - x^109*y + x^109*z0 - x^108*z0^2 + x^108*y + x^108*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 - x^107 + x^106*y - x^105*y*z0 - x^105*z0^2 - x^105*z0 - x^104*y*z0 + x^104*z0^2 + x^105 + x^104*y - x^104*z0 - x^104 - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^103 + x^101*z0^2 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 + x^100*y - x^100*z0 + x^99*y*z0 - x^98*y*z0^2 - x^100 + x^99*y + x^98*y*z0 - x^97*y*z0^2 + x^98*y - x^98*z0 - x^97*y*z0 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 - x^97 + x^95*z0^2 - x^94*y*z0^2 + x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y + x^94*z0 - x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*z0 - x^89*y*z0 - x^89*z0^2 - x^88*y*z0^2 - x^90 - x^89*z0 - x^88*y*z0 + x^88*z0^2 + x^88*y + x^88*z0 + x^86*y*z0^2 + x^88 + x^87*y + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^85*y + x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^85 + x^84*z0 - x^83*y*z0 - x^84 + x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^81*z0 + x^80*y*z0 + x^80*z0^2 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^80 + x^79*y + x^79*z0 + x^78*z0^2 - x^79 + x^78*y - x^78*z0 - x^76*y*z0^2 + x^77*y - x^77*z0 - x^76*y*z0 - x^76*z0^2 - x^75*y*z0^2 + x^77 + x^76*y - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 + x^74*y - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^70*y + x^69*y*z0 + x^69*z0^2 + x^69*y - x^69*z0 - x^68*y*z0 - x^68*z0^2 + x^68*y + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^64*z0^2 - x^63*y*z0^2 + x^64*z0 - x^64 + x^62*y*z0 - x^61*y*z0^2 - x^62*y - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^60*y*z0 + x^60*y - x^60*z0 - x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^58*z0^2 - x^58*y + x^58*z0 + x^57*z0^2 - x^56*y*z0^2 - x^58 + x^57*y - x^56*y*z0 - x^56*z0^2 - x^56*y + x^55*y*z0 - x^56 + x^51,
 x^115 - x^114*z0 + x^113*z0^2 - x^113*z0 + x^113 - x^112*y + x^111*y*z0 - x^110*y*z0^2 - x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^110*y - x^109*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 - x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^107 + x^106*y + x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^105 + x^103*z0^2 - x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^103 + x^101*y*z0 + x^100*y*z0^2 + x^102 + x^101*z0 - x^100*y*z0 - x^100*y - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 + x^98*z0^2 + x^97*y*z0^2 + x^99 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 + x^95*y*z0^2 - x^97 + x^96*y + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 - x^94*z0 + x^93*y*z0 + x^94 + x^93*y - x^93*z0 - x^92*y*z0 + x^91*y*z0^2 - x^93 + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^91*z0 + x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 - x^90*z0 + x^88*y*z0^2 - x^90 + x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^89 - x^88*y + x^86*y*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 + x^87 + x^86*z0 + x^85*y*z0 - x^85*z0^2 + x^86 + x^84*z0^2 - x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*z0^2 - x^83 + x^82*y - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 + x^81*z0 + x^80*y*z0 + x^80*y + x^79*z0^2 - x^80 + x^79*z0 + x^77*y*z0^2 + x^79 - x^77*y*z0 + x^77*z0^2 + x^77*y + x^76*z0^2 + x^77 - x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^76 - x^75*y + x^75*z0 - x^74*z0 + x^73*z0^2 + x^72*y*z0^2 + x^73*y - x^73*z0 + x^72*y*z0 + x^73 - x^71*y*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*z0 - x^70*y*z0 - x^69*y*z0^2 - x^71 - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 - x^69*z0 - x^68*y*z0 - x^69 - x^68*y - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y + x^63*y*z0 + x^63*z0^2 - x^64 - x^63*y - x^62*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*z0 - x^59*y*z0^2 - x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^59 - x^57*z0^2 - x^56*y*z0^2 + x^57*z0 - x^56*z0^2 + x^57 - x^56*y + x^55*y*z0 - x^56 + x^55*y + x^51*z0,
 -x^113*z0 - x^112*z0^2 + x^113 + x^111*z0^2 - x^111*z0 + x^110*y*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 - x^110*y - x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*y + x^106*y*z0^2 - x^108 + x^106*y*z0 + x^107 + x^106*z0 + x^105*y*z0 + x^104*y*z0^2 + x^106 + x^105*z0 + x^104*y*z0 + x^104*z0^2 + x^104*y + x^104*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^101*z0^2 - x^101*y + x^101*z0 - x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^100*y + x^100*z0 + x^98*y*z0^2 - x^100 - x^99*z0 + x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 - x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 - x^92*y*z0^2 + x^94 - x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*z0^2 - x^90*y*z0^2 + x^92 - x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*y + x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 - x^89 + x^88*z0 + x^87*z0^2 + x^88 - x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 + x^85*y - x^85*z0 + x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 + x^85 - x^83*y*z0 - x^83*z0^2 + x^82*y*z0^2 + x^83*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^82*z0 - x^81*z0^2 + x^82 + x^81*z0 + x^80*y*z0 - x^80*z0^2 - x^79*y*z0^2 + x^80*y - x^79*y*z0 - x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y + x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^76*y + x^76*z0 - x^76 + x^75*z0 - x^74*z0^2 + x^73*y*z0^2 + x^74*z0 + x^73*y*z0 + x^73*z0^2 - x^73*y - x^72*y*z0 - x^72*z0^2 - x^72*y + x^72*z0 - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*y - x^70*z0 + x^68*y*z0^2 - x^70 - x^69*y + x^68*z0^2 - x^67*y*z0^2 - x^68*y - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 - x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 - x^65*y + x^64*y*z0 + x^64*z0^2 + x^64*y - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 + x^61*z0^2 - x^62 + x^61*z0 + x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60 + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^55*y*z0^2 - x^57 - x^56*y + x^55*y*z0 - x^55*y + x^51*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 - x^111*z0^2 + x^110*y*z0^2 - x^111*y + x^110*y*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^108 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 - x^105*y*z0 + x^106 + x^105*y + x^105*z0 + x^104*y*z0 - x^103*y*z0^2 + x^104*y + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102 + x^101*y + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 - x^98*y*z0^2 - x^100 - x^99*y + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^98*z0 + x^97*z0^2 + x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y + x^96*z0 - x^95*y*z0 + x^94*y*z0^2 - x^96 + x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*y - x^91*y*z0 + x^91*z0^2 + x^92 - x^91*y + x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^90*z0 - x^90 + x^89*y + x^88*y*z0 - x^89 - x^88*y - x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y + x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*z0 + x^85*y*z0 + x^85*y + x^84*z0^2 - x^85 + x^84*y - x^84*z0 - x^83*y*z0 + x^83*z0^2 + x^84 + x^83*y - x^81*y*z0^2 + x^83 + x^82*y - x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^80*y - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^78*z0 - x^77*y*z0 + x^76*y*z0 + x^75*y*z0^2 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^75*z0 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 + x^73*z0^2 + x^72*y*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^73 + x^72*z0 - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^71*z0 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 - x^70*y - x^70*z0 - x^70 - x^69*y - x^69*z0 - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^67*z0^2 + x^66*y*z0^2 - x^67*z0 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*y*z0 - x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 + x^63 - x^62*y + x^61*z0^2 + x^60*y*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y - x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 - x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*y - x^56*z0^2 - x^55*y*z0^2 - x^56*y + x^55*y*z0 - x^55*y + x^51*y,
 -x^115 + x^113*z0^2 + x^114 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*z0^2 + x^108*y*z0^2 - x^108*z0^2 + x^107*y*z0^2 - x^108*y - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y + x^107*z0 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 - x^104*y*z0^2 + x^106 - x^104*y - x^104*z0 + x^103*y*z0 - x^103*z0^2 + x^102*y*z0^2 + x^103*y + x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^102*y + x^102*z0 - x^102 - x^101*z0 - x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^100*z0 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 - x^98*z0 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 - x^95*y*z0^2 + x^97 + x^96*y - x^95*y*z0 - x^94*y*z0^2 + x^96 - x^95*y + x^94*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y - x^91*y*z0^2 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 - x^89*y*z0 + x^89*y + x^89*z0 - x^88*z0^2 + x^89 - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^88 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 + x^85*y - x^85*z0 - x^84*z0^2 + x^83*y*z0^2 - x^85 + x^84*y + x^84*z0 - x^83*y*z0 + x^84 - x^83*z0 + x^82*y*z0 - x^81*y*z0^2 - x^83 + x^82*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*z0^2 - x^78*y*z0^2 - x^80 + x^79*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^78 - x^77*y + x^76*y*z0 - x^75*y*z0^2 - x^77 - x^76*y - x^76*z0 + x^75*y*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 - x^74*z0 - x^73*z0^2 + x^72*y*z0^2 - x^73*z0 + x^72*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*y*z0 - x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^71 + x^70*y - x^70*z0 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y + x^67*z0 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y - x^64*z0^2 - x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^63 + x^62*y + x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 - x^59*y - x^58*y*z0 + x^58*z0^2 + x^59 + x^58*y + x^58*z0 + x^57*y*z0 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 + x^55*y*z0 + x^56 + x^51*y*z0,
 -x^115 + x^114*z0 - x^113*z0^2 - x^113*z0 + x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^110*y*z0^2 - x^112 + x^111*z0 + x^110*y*z0 - x^109*y*z0^2 - x^111 + x^110*y + x^109*z0^2 - x^110 + x^109*y + x^109*z0 - x^108*y*z0 + x^109 + x^108*y - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^108 - x^107*y + x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 + x^104*y*z0 + x^103*y*z0^2 + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 - x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^101 - x^100*y + x^100*z0 - x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y - x^98*z0^2 - x^97*y*z0^2 - x^99 - x^98*z0 + x^97*z0^2 - x^98 - x^97*y - x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^96*y + x^96*z0 - x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 + x^92*y*z0^2 + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 + x^92*z0 + x^91*y*z0 - x^92 - x^90*z0^2 - x^91 - x^90*y + x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^89*y + x^88*y*z0 - x^88*y - x^87*y*z0 + x^87*z0^2 - x^88 + x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y + x^85*y*z0 - x^86 + x^85*y - x^84*y*z0 + x^84*z0^2 + x^85 + x^84*z0 - x^83*z0^2 - x^84 + x^83*y - x^83*z0 + x^82*z0^2 + x^81*y*z0^2 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 + x^79*y + x^78*y*z0 - x^78*z0^2 + x^79 + x^78*y - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*z0 - x^76*y*z0 + x^76*z0^2 + x^75*y*z0^2 - x^77 + x^75*z0^2 - x^76 + x^74*y*z0 - x^74*z0^2 + x^74*z0 + x^73*y*z0 - x^74 - x^73*y - x^72*y*z0 + x^71*y*z0^2 - x^72*y - x^71*y*z0 - x^71*z0^2 - x^71*y + x^71*z0 + x^70*y*z0 - x^71 + x^70*y + x^70*z0 + x^68*y*z0^2 + x^70 - x^69*y - x^68*y*z0 + x^68*z0^2 - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 - x^66*z0^2 - x^67 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y + x^61*y*z0 - x^60*y*z0^2 + x^62 + x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y + x^60*z0 + x^59*y*z0 + x^59*z0^2 + x^60 + x^58*z0^2 - x^57*y*z0^2 - x^59 + x^58*y + x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 + x^55*y*z0 - x^56 - x^55*y + x^51*y*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 - x^114 - x^112*z0^2 - x^113 + x^112*y - x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 + x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 + x^109*z0^2 - x^108*y*z0^2 + x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*y - x^108*z0 - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 + x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 + x^106*y - x^106*z0 + x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 - x^104*y*z0 - x^103*y*z0^2 + x^105 - x^104*z0 - x^103*y*z0 - x^104 - x^103*y - x^102*y*z0 + x^102*z0^2 + x^103 - x^102*z0 - x^101*y*z0 - x^102 + x^100*z0^2 - x^99*y*z0^2 + x^101 + x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*z0^2 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*z0 + x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 - x^93*z0^2 - x^93*y - x^93*z0 - x^92*y*z0 - x^92*z0^2 + x^92*y + x^92*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^90*y + x^89*y*z0 - x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 + x^89 - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^86*y*z0^2 - x^88 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y + x^86*z0 - x^85*y*z0 - x^84*y*z0^2 + x^86 + x^84*z0^2 - x^83*y*z0^2 - x^85 - x^84*y + x^83*y*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 + x^83*z0 + x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^81*z0^2 + x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 + x^79*y*z0 + x^79*z0^2 + x^80 - x^79*y - x^79*z0 - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^78*y - x^77*z0^2 - x^76*y*z0^2 + x^77*y - x^76*z0^2 + x^75*y*z0^2 - x^74*y*z0 + x^73*y*z0^2 - x^74*y + x^74*z0 - x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 - x^72*z0^2 - x^71*y*z0^2 - x^72*y + x^72*z0 - x^70*y*z0^2 + x^71*z0 - x^70*y*z0 + x^70*z0^2 + x^70*y - x^70*z0 + x^69*y*z0 + x^68*y*z0^2 - x^70 - x^69*y - x^69*z0 - x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 + x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^65*y*z0^2 + x^67 + x^66*z0 + x^65*y + x^65*z0 + x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 + x^62*z0 + x^61*y*z0 + x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 - x^61 - x^60*y + x^60*z0 - x^59*z0^2 + x^58*y*z0^2 - x^60 - x^59*y + x^59*z0 + x^58*y*z0 - x^57*y*z0^2 + x^58*y + x^57*z0^2 + x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*y*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 + x^56*y - x^56 + x^55*y + x^52,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 + x^113 - x^112*y - x^112*z0 + x^111*y*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*y - x^111*z0 + x^110*y*z0 + x^110*z0^2 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^110 - x^109*z0 + x^108*y*z0 - x^107*y*z0^2 - x^108*z0 + x^107*y*z0 - x^107*z0^2 - x^106*y*z0^2 - x^107*z0 - x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 + x^106*y - x^106*z0 + x^105*y - x^105*z0 - x^105 - x^104*y + x^104*z0 + x^102*y*z0^2 + x^103*z0 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 + x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 + x^100*y + x^100*z0 + x^99*z0^2 - x^98*y*z0^2 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 - x^98 - x^97*z0 - x^96*y*z0 - x^95*y*z0^2 + x^97 + x^96*z0 + x^94*y*z0^2 - x^96 + x^95*y - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 + x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^94 - x^93*y - x^91*y*z0^2 - x^92*y - x^92*z0 - x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 - x^92 + x^91*z0 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 - x^90 + x^88*y*z0 + x^88*z0^2 - x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^84*y*z0^2 - x^86 - x^85*y + x^84*y*z0 - x^84*y + x^83*z0^2 - x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^80*y*z0^2 + x^82 - x^80*y*z0 + x^80*y + x^80*z0 - x^79*y*z0 + x^79*z0^2 - x^78*y*z0^2 + x^80 + x^79*y + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^77*z0^2 - x^78 - x^77*y - x^77*z0 - x^76*z0^2 - x^77 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*y - x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y + x^73*z0 + x^72*y*z0 + x^72*z0^2 - x^71*y*z0^2 - x^72*y - x^72*z0 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 + x^70*y*z0 - x^70*z0^2 + x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0^2 + x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y + x^68*z0 - x^67*y*z0 + x^67*z0^2 - x^67*y + x^66*z0^2 + x^65*y*z0^2 + x^67 + x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^65*y + x^64*y*z0 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 + x^63*y*z0 - x^62*y*z0^2 + x^64 - x^63*y + x^62*z0^2 + x^62*z0 - x^61*y*z0 + x^62 - x^61*y - x^61*z0 - x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 + x^61 - x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^60 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y + x^57*z0 - x^55*y*z0^2 + x^57 + x^56*z0 + x^56 + x^52*z0,
 x^115 + x^114*z0 - x^114 + x^113*z0 - x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 - x^110*z0^2 - x^111 + x^110*y + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y + x^108*z0 - x^106*y*z0^2 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^106*z0 - x^106 - x^105*y - x^105*z0 - x^104*y*z0 + x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^102*y*z0^2 - x^103*y - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 - x^101*y*z0 - x^100*y*z0^2 + x^102 + x^101*y - x^101*z0 - x^100*y*z0 - x^100*y - x^98*y*z0^2 + x^100 - x^99*y + x^99*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 + x^98*y - x^96*y*z0^2 - x^98 - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 + x^97 - x^96*z0 + x^95*y*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^93*y*z0^2 + x^95 - x^94*y + x^94*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 + x^93 - x^92*y + x^92*z0 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 - x^88*y*z0^2 - x^89*y - x^89*z0 - x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^88 + x^87*y + x^87*z0 + x^87 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 + x^86 + x^85*z0 - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 + x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*y + x^79*y*z0 - x^79*z0^2 + x^80 + x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 - x^79 + x^78*y - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^77 + x^75*z0^2 - x^74*y*z0^2 - x^76 - x^75*z0 + x^74*y*z0 + x^74*z0^2 - x^73*y*z0^2 + x^75 + x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 - x^72*z0 - x^70*y*z0^2 + x^71*y + x^70*y*z0 - x^70*z0^2 - x^71 - x^70*y - x^70*z0 + x^69*z0^2 - x^68*y*z0 - x^67*y*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*z0^2 + x^65*y + x^64*y*z0 - x^64*z0^2 - x^65 - x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^63*y + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 - x^62*z0 - x^61*y*z0 - x^60*y*z0^2 - x^62 + x^61*z0 - x^60*y*z0 - x^59*y*z0^2 + x^61 + x^60*z0 + x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^55*y*z0^2 + x^56*y + x^55*y*z0 + x^56 + x^52*z0^2,
 -x^115 + x^113*z0^2 + x^112*y + x^111*z0^2 - x^110*y*z0^2 - x^112 + x^111*z0 - x^110*z0^2 - x^109*z0^2 - x^108*y*z0^2 + x^109*y + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 + x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^106*y*z0 - x^105*y*z0^2 + x^106*y + x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^106 + x^104*z0^2 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 - x^101*y + x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^101 + x^100*y - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^98*y*z0^2 + x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^97*y*z0^2 - x^99 - x^96*y*z0^2 - x^97*y + x^97*z0 - x^96*y*z0 + x^96*z0^2 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*z0 - x^94*z0^2 - x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*z0^2 + x^92*y*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^93 - x^92*z0 - x^91*z0^2 - x^90*y*z0^2 - x^90*z0^2 + x^89*y*z0^2 - x^90*y + x^90 - x^89*z0 + x^88*z0^2 - x^89 + x^88*z0 + x^87*y*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 - x^86*y*z0 - x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 - x^85 + x^84*y + x^84*z0 + x^83*z0^2 + x^83*z0 - x^83 - x^82*y + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y + x^81*z0 + x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80 - x^78*z0^2 - x^77*y*z0^2 - x^79 - x^78*y + x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 + x^76*y*z0 + x^77 - x^76*y - x^76*z0 + x^75*z0 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^75 - x^74*y + x^74*z0 + x^73*z0^2 + x^72*y*z0^2 - x^74 + x^73*y + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y + x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 - x^67*y*z0^2 - x^67*y*z0 - x^67*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 + x^66*y + x^66*z0 - x^64*y*z0^2 - x^66 - x^65*y - x^64*z0^2 - x^63*y*z0^2 - x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^63*z0 - x^62*z0^2 - x^63 + x^62*y - x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 - x^61 + x^60*y - x^60*z0 - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 - x^59*y - x^59*z0 - x^58*y*z0 - x^57*y*z0^2 - x^59 + x^58*z0 + x^57*y*z0 - x^56*y*z0^2 + x^58 + x^57*y + x^57*z0 - x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*z0 + x^56 + x^52*y,
 -x^115 - x^114*z0 + x^114 - x^112*z0^2 + x^112*y + x^112*z0 + x^111*y*z0 - x^112 - x^111*y - x^111*z0 - x^110*z0^2 + x^109*y*z0^2 + x^110*z0 - x^109*y*z0 + x^109*y - x^109*z0 + x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 + x^109 + x^108*z0 - x^107*y*z0 - x^108 + x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y + x^106*z0 + x^104*y*z0^2 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^103*y*z0 + x^102*y*z0^2 + x^103*y + x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 + x^103 + x^102*y + x^102*z0 + x^100*y*z0^2 - x^102 - x^101*y - x^100*y*z0 + x^100*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^99*y - x^99*z0 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^97*y + x^96*z0^2 + x^95*y*z0^2 - x^97 - x^96*y + x^96*z0 + x^95*y*z0 + x^94*y*z0^2 + x^96 - x^95*y - x^95*z0 - x^94*z0^2 + x^93*y*z0^2 - x^95 + x^93*z0^2 - x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 - x^92*y + x^91*z0^2 - x^90*y*z0^2 - x^92 - x^91*y + x^89*y*z0^2 + x^91 + x^90*y + x^89*y*z0 + x^89*z0^2 + x^89*z0 + x^87*y*z0^2 - x^88*y + x^87*y*z0 - x^87*z0^2 + x^87*y + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^84*y*z0^2 - x^86 - x^85*y + x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^83*y*z0 - x^82*y*z0^2 - x^83*y - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 + x^81*y + x^81*z0 + x^80*z0^2 - x^79*y*z0^2 + x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 - x^80 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*y - x^78*z0 + x^77*y*z0 + x^77*z0^2 - x^77*y + x^77*z0 - x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 - x^76*y + x^76*z0 + x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 - x^74*y*z0 + x^73*y*z0^2 + x^73*y*z0 + x^73*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^71*y*z0^2 - x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 - x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^69 - x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 + x^67*y - x^67*z0 + x^65*y*z0^2 + x^67 + x^66*z0 + x^65*y*z0 - x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 - x^65 - x^64*y + x^64*z0 - x^63*y*z0 - x^62*y*z0^2 - x^64 + x^63*y + x^62*y*z0 + x^62*z0^2 - x^63 - x^62*z0 + x^61*y*z0 - x^61*z0^2 - x^60*y*z0^2 + x^62 + x^61*y + x^60*y*z0 + x^59*y*z0^2 - x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 + x^59 - x^58*z0 + x^57*y*z0 + x^56*y*z0^2 - x^57*y + x^57 - x^56*y + x^55*y*z0 + x^56 + x^55*y + x^52*y*z0,
 -x^115 + x^113*z0^2 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 + x^111*z0^2 - x^110*y*z0^2 - x^111*z0 + x^110*z0^2 + x^109*y*z0^2 + x^111 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^108*y*z0^2 - x^110 + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^107*y*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 + x^107 - x^106*y - x^105*y*z0 + x^105*z0^2 - x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 - x^105 - x^103*z0^2 - x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 + x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^98*y*z0^2 - x^100 - x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 + x^99 + x^98*y - x^97*y*z0 - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^97 + x^96*y - x^96*z0 + x^95*y*z0 - x^95*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 - x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^94 - x^93*y - x^93*z0 + x^92*y*z0 + x^91*y*z0^2 - x^92*z0 + x^91*y*z0 + x^91*z0^2 + x^92 + x^91*z0 - x^90*y*z0 + x^90*z0^2 + x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 - x^89*y*z0 + x^89*z0^2 - x^89*y - x^89*z0 - x^87*y*z0^2 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 + x^88 + x^87*y - x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*z0^2 + x^85 + x^84*y + x^84*z0 + x^83*y*z0 - x^84 - x^83*y - x^82*z0^2 - x^81*y*z0^2 - x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 + x^82 + x^81*y - x^81*z0 - x^79*y*z0^2 + x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^78*y*z0^2 - x^80 + x^79*z0 + x^78*y*z0 - x^78*z0^2 + x^79 - x^77*y*z0 - x^77*z0^2 + x^78 + x^77*y - x^77*z0 + x^76*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 + x^76 + x^74*y*z0 - x^74*z0^2 + x^73*y*z0^2 - x^73*y*z0 + x^73*z0^2 - x^74 + x^73*z0 - x^72*y*z0 - x^72*y + x^70*y*z0^2 + x^72 - x^71*y + x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 - x^69*y + x^69*z0 + x^68*y*z0 + x^67*y*z0^2 - x^69 - x^68*y - x^66*y*z0^2 + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 + x^64*z0 - x^62*y*z0^2 + x^64 - x^63*y + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^63 - x^62*y - x^62*z0 + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 + x^61*y + x^59*y*z0^2 - x^61 + x^60*z0 + x^58*y*z0 + x^57*y*z0^2 + x^59 + x^58*y - x^58*z0 - x^57*z0^2 + x^58 + x^56*y*z0 - x^56*z0^2 - x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^52*y*z0^2,
 x^115 + x^114*z0 - x^114 + x^113*z0 - x^112*z0^2 + x^113 - x^112*y - x^112*z0 - x^111*y*z0 + x^111*z0^2 + x^111*y - x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 - x^110*y - x^110*z0 + x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 - x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^108*y + x^108*z0 + x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^107*y + x^107*z0 - x^105*y*z0^2 + x^107 + x^105*z0^2 + x^105*z0 - x^104*y*z0 - x^105 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^102*z0 + x^101*y*z0 - x^102 - x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 - x^99*y*z0^2 - x^101 - x^100*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*z0 + x^98*y*z0 + x^99 - x^98*z0 - x^97*z0^2 + x^96*y*z0^2 - x^97*z0 + x^96*y*z0 - x^95*y*z0^2 + x^97 + x^96*z0 - x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*y - x^93*z0^2 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^91 + x^90*y + x^90*z0 + x^89*y*z0 - x^88*y*z0^2 - x^90 + x^89*y - x^88*z0^2 + x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 - x^86*y*z0 - x^86*z0^2 + x^85*y*z0^2 - x^87 - x^86*y + x^86*z0 - x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*z0 + x^83*y*z0 + x^83*z0^2 - x^83*y + x^83*z0 - x^82*y*z0 - x^82*z0^2 + x^81*y*z0^2 - x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^81*y - x^80*y*z0 - x^80*z0^2 - x^81 - x^80*y + x^80*z0 - x^79*y*z0 - x^79*z0^2 + x^78*y*z0^2 + x^80 - x^79*z0 - x^78*z0^2 - x^77*y*z0^2 - x^79 + x^78*y - x^77*y*z0 - x^77*z0^2 + x^76*y*z0^2 - x^78 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 - x^77 + x^76*z0 - x^75*y*z0 + x^74*y*z0^2 - x^76 + x^75*y - x^75*z0 - x^74*z0^2 - x^73*y*z0^2 - x^75 + x^74*y - x^73*z0^2 + x^72*y*z0 + x^72*z0^2 + x^71*y*z0^2 + x^73 + x^72*y + x^72*z0 + x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 - x^70*y*z0 - x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^69*y*z0 - x^69*z0^2 + x^68*y*z0^2 + x^69*y + x^69*z0 - x^68*y*z0 + x^69 + x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y + x^66*z0^2 + x^66*y + x^66*z0 + x^64*y*z0^2 - x^66 - x^65*z0 - x^64*y*z0 - x^64*z0^2 - x^63*y*z0^2 - x^65 - x^64*z0 + x^63*z0^2 - x^62*y*z0^2 + x^64 + x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 + x^62*y - x^62*z0 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 + x^62 - x^61*y - x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 - x^60*z0 + x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y + x^59*z0 + x^58*z0^2 - x^59 + x^58*y + x^58*z0 - x^57*y*z0 + x^57*z0^2 + x^58 + x^57*y - x^57*z0 + x^56*y*z0 - x^56*z0^2 - x^57 - x^56*z0 + x^55*y*z0 + x^55*y + x^53,
 x^115 - x^113*z0^2 + x^112*z0^2 - x^112*y - x^111*z0^2 + x^110*y*z0^2 - x^112 - x^111*z0 - x^110*z0^2 - x^109*y*z0^2 + x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^108*y*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*z0 + x^107*z0^2 + x^108 + x^107*y + x^106*y*z0 - x^106*y + x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^105*y + x^104*z0^2 + x^105 + x^104*y + x^104*z0 - x^103*z0^2 + x^104 + x^103*y - x^103*z0 + x^102*y*z0 + x^102*y + x^101*z0^2 + x^102 + x^101*y + x^101*z0 + x^100*y*z0 - x^100*z0^2 + x^99*y*z0^2 + x^101 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 - x^100 + x^99*y + x^99*z0 + x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^96*z0 + x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 + x^96 + x^95*y + x^95*z0 - x^94*z0^2 + x^93*y*z0^2 + x^95 - x^94*y - x^94*z0 - x^93*y*z0 + x^92*y*z0^2 - x^94 - x^92*y*z0 - x^92*z0^2 - x^92*z0 - x^91*y*z0 + x^91*z0^2 + x^90*y*z0^2 - x^92 + x^91*y + x^91*z0 + x^90*z0^2 - x^91 + x^89*y*z0 + x^89*z0^2 + x^88*y*z0^2 - x^89*y + x^88*y*z0 - x^88*z0^2 - x^87*y*z0^2 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y + x^87*z0 + x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*y - x^84*z0^2 - x^84*y - x^82*y*z0^2 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 + x^81*y + x^81*z0 + x^80*z0^2 + x^81 - x^80*z0 + x^79*y*z0 - x^78*y*z0^2 - x^80 - x^79*y + x^79*z0 - x^78*y*z0 + x^78*z0^2 + x^79 - x^78*y - x^78*z0 - x^77*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*z0^2 - x^76*y + x^75*z0^2 - x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^73*y*z0^2 - x^75 + x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*z0 + x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^73 - x^72*z0 - x^71*z0^2 - x^71*y - x^71 - x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 - x^68*z0^2 - x^69 + x^68*y - x^68*z0 + x^67*y*z0 - x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^66*y - x^66*z0 - x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^65*z0 + x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^63*z0^2 + x^64 + x^63*z0 + x^62*z0^2 - x^61*y*z0^2 - x^63 - x^61*z0^2 + x^62 + x^61*y + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^61 - x^60*y - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^58*y - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*z0 + x^56*y*z0 - x^56*z0^2 + x^55*y + x^53*z0,
 -x^112*z0^2 - x^113 - x^112*z0 - x^111*z0^2 + x^112 - x^111*z0 + x^109*y*z0^2 + x^111 + x^110*y - x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y + x^109*z0 + x^108*y*z0 + x^108*z0^2 - x^108*y - x^108*z0 + x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 - x^105*y*z0^2 - x^107 - x^106*z0 + x^105*y*z0 - x^104*y*z0^2 - x^106 - x^104*z0^2 - x^103*y*z0^2 - x^105 + x^104*y - x^103*z0^2 + x^102*y*z0^2 - x^103*y - x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 + x^101*y + x^100*z0^2 - x^99*y*z0^2 - x^100*z0 - x^99*y*z0 - x^100 + x^99*y - x^99*z0 + x^98*z0^2 - x^97*y*z0^2 + x^99 - x^98*y + x^98*z0 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 + x^96*y*z0 + x^95*y*z0^2 + x^97 - x^96*z0 - x^95*y*z0 - x^96 + x^95*y - x^94*y*z0 - x^94*z0^2 - x^93*y*z0^2 + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^94 + x^93*y + x^93*z0 - x^92*y*z0 + x^92*z0^2 - x^91*y*z0^2 - x^93 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 + x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^89*y*z0 + x^89*z0^2 - x^90 - x^89*y - x^88*z0^2 - x^87*y*z0^2 + x^89 - x^88*y - x^88*z0 + x^87*y*z0 + x^87*z0^2 + x^86*y*z0^2 - x^88 - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 - x^86 + x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y + x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 + x^84 - x^83*z0 + x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 - x^81*z0 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*y + x^79*z0^2 - x^79*z0 + x^78*y*z0 + x^78*z0^2 + x^77*y*z0^2 + x^79 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 - x^75*y*z0^2 - x^76*z0 + x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*y + x^75*z0 + x^74*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^73*z0 - x^72*z0^2 + x^72*y - x^72*z0 + x^70*y*z0^2 + x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 + x^68*y*z0^2 + x^68*y*z0 - x^68*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^67*y + x^67*z0 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 - x^65*y*z0 - x^64*y*z0^2 + x^66 + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 - x^64*y + x^64*z0 + x^62*y*z0^2 + x^63*z0 - x^62*y*z0 - x^61*y*z0^2 + x^63 - x^62*y - x^61*z0^2 - x^60*y*z0^2 + x^62 - x^60*y*z0 - x^60*z0^2 + x^59*y*z0^2 + x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 - x^59*y + x^59*z0 + x^58*y*z0 - x^58*z0^2 - x^57*y*z0^2 - x^59 - x^58*y - x^58*z0 + x^57*y*z0 - x^57*z0^2 + x^56*y*z0 + x^56*z0^2 + x^56*z0 + x^53*z0^2,
 -x^115 + x^113*z0^2 - x^113*z0 - x^112*z0^2 + x^112*y + x^112*z0 - x^110*y*z0^2 + x^112 + x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^109*y*z0 + x^109*z0^2 - x^109*y + x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 - x^108*z0 - x^107*z0^2 - x^106*y*z0^2 + x^107*y - x^107*z0 - x^106*y*z0 - x^106*z0^2 + x^105*y*z0^2 - x^106*y + x^106*z0 - x^105*y*z0 + x^104*y*z0^2 + x^106 + x^104*y*z0 + x^104*z0^2 - x^103*y*z0^2 - x^105 - x^104*y + x^104*z0 + x^103*z0^2 + x^104 + x^103*y - x^103*z0 - x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 + x^103 + x^102*y - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^102 + x^100*y*z0 + x^100*z0^2 - x^99*y*z0^2 - x^100*z0 + x^99*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y - x^98*z0 + x^97*z0^2 + x^96*y*z0^2 - x^98 - x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 - x^97 + x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^93*y*z0^2 - x^95 - x^94*y + x^94*z0 - x^93*y*z0 - x^93*z0^2 + x^92*y*z0^2 + x^94 - x^93*z0 + x^91*y*z0^2 + x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y - x^90*y*z0 + x^90*z0^2 + x^91 + x^90*y + x^89*z0^2 + x^88*y*z0^2 + x^90 + x^89*y - x^89*z0 + x^88*z0^2 + x^87*y*z0^2 - x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^87*z0^2 - x^87*y - x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*z0 - x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^86 - x^85*z0 - x^84*y*z0 + x^83*y*z0^2 - x^84*z0 - x^83*y*z0 + x^83*z0^2 - x^82*y*z0^2 - x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 - x^82*y + x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 + x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 + x^80*y + x^79*y*z0 - x^79*z0^2 - x^79*y - x^78*y*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y - x^78*z0 + x^77*z0^2 + x^78 - x^77*y - x^76*y*z0 - x^76*z0^2 + x^77 - x^76*y - x^76*z0 + x^75*y*z0 + x^74*y*z0^2 + x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 + x^72*y*z0^2 + x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*y - x^70*y*z0 + x^69*y*z0^2 - x^71 + x^70*y + x^70*z0 + x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 - x^68*z0^2 + x^69 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y + x^67*z0 - x^66*z0^2 - x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^66 + x^65*z0 + x^64*y*z0 + x^63*y*z0^2 + x^64*y + x^64*z0 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 - x^62*y - x^61*y*z0 - x^60*y*z0^2 + x^61*z0 - x^60*y*z0 + x^60*z0^2 - x^59*y*z0^2 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 + x^57*y*z0^2 + x^58*y - x^58*z0 - x^57*z0^2 - x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 - x^56*z0^2 + x^55*y*z0^2 + x^57 - x^56*y - x^56*z0 - x^55*y*z0 + x^56 + x^55*y + x^53*y,
 -x^115 + x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^112 + x^111*y + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 - x^110*y - x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^110 - x^109*y - x^109*z0 + x^107*y*z0^2 - x^109 - x^108*z0 - x^107*z0^2 + x^106*y*z0^2 - x^107*y + x^106*y*z0 - x^106*z0^2 - x^105*y*z0^2 - x^106*z0 - x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 - x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 + x^104*y - x^103*z0^2 - x^103*z0 + x^102*y*z0 - x^102*z0^2 - x^102*y - x^102*z0 + x^101*y*z0 - x^100*y*z0^2 - x^101*y + x^101*z0 - x^100*z0^2 - x^99*y*z0^2 + x^101 + x^100*y - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 + x^99*z0 + x^98*z0^2 - x^97*y*z0 + x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*y - x^97*z0 + x^96*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*y*z0 - x^96 + x^95*y - x^95*z0 - x^94*y*z0 + x^93*y*z0^2 + x^95 + x^94*y - x^94*z0 + x^93*y*z0 + x^93*z0^2 + x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 - x^93 + x^92*z0 - x^92 + x^91*y + x^91*z0 - x^90*y*z0 - x^89*y*z0^2 + x^90*z0 + x^89*z0^2 + x^90 + x^89*y - x^89*z0 - x^88*y*z0 + x^87*y*z0^2 - x^89 - x^88*y + x^88*z0 + x^87*y*z0 + x^86*y*z0^2 + x^87*y + x^86*y*z0 - x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*z0 - x^84*z0^2 - x^85 - x^84*y - x^84*z0 + x^83*z0^2 - x^84 + x^83*y + x^82*y*z0 + x^82*z0^2 - x^83 + x^82*y - x^82*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y + x^81*z0 + x^80*y*z0 - x^81 + x^80*y - x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^78*y*z0 - x^79 + x^78*y - x^78*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 + x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^77 - x^76*z0 + x^75*z0^2 + x^75*z0 - x^74*z0^2 + x^75 + x^74*z0 - x^73*y*z0 - x^72*y*z0^2 - x^72*y*z0 - x^72*y - x^72*z0 - x^71*y*z0 - x^71*z0^2 + x^70*y*z0^2 - x^72 + x^71*z0 + x^69*y*z0^2 + x^71 - x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 - x^69*y - x^69*z0 + x^68*y*z0 + x^67*y*z0^2 + x^68*z0 + x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 - x^68 - x^67*y - x^65*y*z0^2 - x^67 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*y*z0 - x^65 - x^63*z0^2 - x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*z0 - x^61*y*z0 + x^62 - x^61*z0 - x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 - x^57*y*z0 + x^56*y*z0^2 - x^58 - x^57*y + x^57*z0 + x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^56*z0 + x^55*y + x^53*y*z0,
 x^115 + x^114*z0 - x^114 + x^112*z0^2 - x^113 - x^112*y + x^112*z0 - x^111*y*z0 + x^111*y - x^111*z0 - x^109*y*z0^2 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 + x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^107*z0^2 + x^106*y*z0^2 + x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 + x^107 - x^106*y - x^106*z0 + x^105*z0^2 + x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 - x^104*z0^2 - x^103*y*z0^2 + x^104*z0 + x^103*y*z0 - x^103*z0^2 - x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 - x^102*z0^2 - x^101*y*z0^2 + x^103 - x^102*z0 + x^101*y*z0 - x^101*z0^2 + x^101*z0 - x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*z0 + x^99*y*z0 - x^99*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^99 + x^98*z0 + x^97*y*z0 + x^96*y*z0^2 - x^98 + x^97*y - x^96*z0^2 - x^95*y*z0^2 - x^97 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y - x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^94*y + x^93*z0^2 + x^93*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*y + x^91*z0 - x^90*y*z0 - x^91 + x^90*y + x^89*y*z0 - x^88*y*z0^2 - x^89*z0 - x^88*y*z0 + x^88*z0^2 - x^87*y*z0^2 - x^89 - x^88*y - x^88*z0 + x^87*z0^2 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^85*y*z0^2 - x^87 + x^86*y - x^86*z0 + x^85*y*z0 - x^86 + x^85*y - x^85*z0 - x^84*y*z0 + x^84*z0^2 + x^83*y*z0^2 - x^85 - x^84*y + x^84*z0 - x^83*y*z0 + x^82*y*z0^2 + x^84 + x^83*y + x^82*y*z0 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 - x^81*y*z0 + x^81*z0^2 + x^80*y*z0^2 - x^82 + x^80*y*z0 + x^80*z0^2 - x^81 + x^80*y - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^80 + x^79*y + x^79*z0 + x^78*z0^2 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^77*y - x^77*z0 + x^75*y*z0^2 + x^76*y + x^76*z0 - x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*y - x^74*z0 + x^73*y*z0 + x^73*z0^2 + x^74 + x^73*y - x^73*z0 + x^72*y*z0 + x^72*z0^2 + x^72*z0 + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y + x^70*y*z0 - x^69*y*z0^2 - x^70*y + x^70*z0 - x^69*y*z0 - x^70 + x^69*y + x^68*y*z0 + x^67*y*z0^2 + x^69 + x^68*y - x^67*y*z0 + x^67*z0^2 - x^66*y*z0^2 + x^67*y - x^67*z0 + x^66*z0^2 + x^67 - x^66*y + x^66*z0 + x^65*z0^2 + x^64*y*z0^2 - x^66 + x^65*y + x^64*y*z0 + x^64*z0^2 - x^63*y*z0^2 - x^64*y - x^64*z0 + x^63*y*z0 - x^63*z0^2 + x^62*y*z0^2 + x^64 - x^61*y*z0^2 + x^62*y - x^61*y*z0 - x^61*z0^2 - x^62 + x^61*y - x^60*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^60 + x^59*y + x^58*y*z0 + x^59 - x^57*y*z0 - x^58 - x^56*z0^2 + x^55*y*z0^2 + x^56*y - x^56*z0 - x^55*y + x^53*y*z0^2,
 x^115 - x^114*z0 + x^113*z0^2 + x^114 + x^113*z0 - x^112*z0^2 - x^113 - x^112*y - x^112*z0 + x^111*y*z0 - x^111*z0^2 - x^110*y*z0^2 - x^111*y + x^111*z0 - x^110*y*z0 + x^109*y*z0^2 + x^111 + x^110*y + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^108*y*z0 + x^108*z0^2 + x^109 - x^108*y - x^108*z0 + x^106*y*z0^2 + x^108 + x^107*y - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^107 + x^105*y*z0 - x^105*z0^2 - x^105*y + x^105*z0 - x^104*z0^2 + x^103*y*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 + x^102*z0^2 - x^101*y*z0^2 - x^103 - x^102*y - x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 - x^102 - x^101*z0 + x^99*y*z0^2 - x^101 - x^100*y + x^100*z0 - x^99*y*z0 + x^98*y*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^99 - x^98*y - x^98*z0 + x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 - x^97*y + x^97*z0 - x^96*y*z0 - x^96*z0^2 + x^97 + x^96*z0 - x^95*y*z0 - x^94*y*z0^2 - x^96 - x^95*z0 - x^94*y*z0 - x^94*z0^2 + x^95 + x^94*z0 + x^93*y*z0 + x^92*y*z0^2 + x^93*y + x^93 + x^92*y + x^92*z0 - x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 + x^92 - x^91*z0 - x^90*y*z0 - x^90*z0^2 - x^91 - x^90*z0 - x^89*y*z0 - x^88*y*z0^2 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 - x^88*z0 + x^87*z0^2 + x^88 + x^87*y + x^87*z0 + x^86*y*z0 + x^86*z0^2 - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^85*y + x^84*y*z0 - x^84*z0^2 + x^84*y + x^84*z0 + x^83*y*z0 + x^82*y*z0^2 - x^84 - x^83*y - x^83*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*z0 - x^81*y*z0 + x^81*z0^2 - x^80*y*z0^2 - x^81*y - x^81*z0 - x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 + x^80*y + x^78*y*z0^2 + x^80 - x^79*z0 + x^78*z0^2 - x^77*y*z0^2 + x^79 + x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 + x^76*y*z0^2 - x^78 - x^77*z0 + x^76*z0^2 + x^75*y*z0^2 + x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 - x^76 + x^75*z0 + x^74*z0^2 - x^75 + x^74*y + x^73*y*z0 + x^73*z0^2 + x^74 - x^73*y - x^73*z0 - x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 - x^70*y*z0^2 + x^72 + x^71*y + x^71*z0 - x^70*z0^2 - x^71 + x^70*y - x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y + x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 + x^68*z0 - x^66*y*z0^2 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^66*y - x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 - x^65*y - x^65*z0 - x^63*y*z0^2 + x^65 + x^64*y - x^64*z0 - x^63*y*z0 + x^62*y*z0^2 - x^63*y - x^63*z0 - x^62*z0^2 - x^61*y*z0^2 - x^63 - x^62*y + x^62*z0 - x^61*y*z0 - x^61*z0 + x^60*y*z0 + x^59*y*z0^2 + x^61 + x^60 - x^59*z0 - x^59 + x^58*y + x^58*z0 + x^57*z0^2 + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^55*y*z0^2 + x^57 + x^56 + x^54,
 -x^115 - x^114*z0 + x^114 - x^112*z0^2 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^112 - x^111*y - x^110*z0^2 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*y*z0 + x^109*z0^2 - x^108*y*z0^2 + x^110 - x^109*y + x^109*z0 + x^108*z0^2 + x^107*y*z0^2 + x^108*y - x^107*y*z0 + x^107*z0^2 - x^106*y*z0^2 - x^108 + x^107*z0 - x^105*y*z0^2 + x^107 + x^105*y*z0 - x^105*z0^2 + x^105*y + x^104*y*z0 - x^104*z0^2 - x^105 - x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 + x^103*z0 - x^102*y*z0 + x^101*y*z0^2 - x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^102 + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y + x^100*z0 + x^99*y*z0 - x^98*y*z0^2 + x^100 + x^99*y - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^98*y + x^98*z0 - x^97*y*z0 - x^97*z0^2 - x^96*y*z0^2 + x^97*y - x^97*z0 - x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y - x^96*z0 - x^95*y*z0 + x^95*z0^2 + x^94*y*z0^2 - x^96 + x^94*y*z0 + x^93*y*z0^2 + x^95 - x^94*y + x^93*y*z0 + x^93*z0^2 + x^94 + x^93*y - x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^93 + x^92*y + x^91*y*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 + x^90*y*z0 - x^90*z0^2 + x^89*y*z0^2 + x^90*y - x^90 + x^89*z0 + x^88*y*z0 - x^87*y*z0^2 + x^89 + x^88*y + x^87*y*z0 - x^87*z0^2 - x^87*z0 - x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^87 - x^86*y + x^86*z0 + x^85*y*z0 - x^85*z0^2 - x^84*y*z0 - x^84*z0^2 + x^85 + x^84*y - x^84*z0 - x^83*z0^2 + x^82*y*z0^2 + x^84 - x^83*y + x^83*z0 + x^82*z0^2 - x^81*y*z0^2 - x^83 - x^82*y - x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^81*y + x^81*z0 - x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*z0 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 + x^79*y + x^79*z0 - x^79 + x^78*y + x^78*z0 + x^77*y*z0 + x^76*y*z0^2 + x^77*y - x^77*z0 + x^76*y*z0 - x^76*z0^2 + x^75*y*z0^2 + x^77 - x^76*y - x^76*z0 - x^75*y*z0 - x^75*z0^2 - x^74*y*z0^2 + x^76 + x^75*z0 - x^74*y*z0 - x^73*y*z0^2 + x^74*y + x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 - x^74 - x^73*z0 + x^72*z0^2 - x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 - x^72 - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 + x^71 - x^70*y + x^70*z0 + x^69*y*z0 + x^69*z0^2 - x^70 - x^69*z0 - x^68*z0^2 - x^67*y*z0^2 - x^69 + x^68*y - x^68*z0 - x^67*z0^2 + x^68 - x^67*y - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^66 + x^65*y + x^65*z0 - x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y + x^64*z0 + x^63*y*z0 - x^63*z0^2 - x^62*y*z0^2 + x^64 - x^63*y + x^62*y*z0 - x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 + x^61*z0^2 - x^60*y*z0^2 - x^61*y + x^61*z0 + x^60*y*z0 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^59*y + x^59*z0 - x^58*z0^2 + x^59 - x^58*y - x^57*y*z0 + x^57*z0^2 + x^56*y*z0^2 - x^57*y - x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0 - x^56 + x^54*z0,
 x^115 + x^114*z0 + x^114 - x^113 - x^112*y - x^112*z0 - x^111*y*z0 - x^111*z0^2 + x^112 - x^111*y + x^111*z0 + x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 + x^108*y*z0^2 - x^109*y - x^108*y*z0 - x^108*z0^2 + x^109 - x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^107*y - x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^107 - x^106*z0 - x^105*z0^2 + x^105*z0 - x^104*y*z0 + x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 - x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y - x^101*y*z0 - x^100*y*z0^2 - x^102 + x^101*y + x^101*z0 - x^100*y*z0 - x^99*y*z0^2 - x^100*z0 - x^99*y*z0 - x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 - x^98 + x^97*y + x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^94*y*z0^2 - x^95*y + x^95*z0 + x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 - x^94*y + x^94*z0 + x^93*z0^2 - x^94 + x^93*z0 + x^92*y*z0 + x^93 - x^92*z0 + x^91*z0^2 + x^90*y*z0^2 + x^92 + x^91*y + x^91*z0 + x^90*y*z0 + x^89*y*z0^2 - x^91 + x^90*y - x^90*z0 + x^89*y*z0 + x^88*y*z0^2 - x^89*y + x^88*y*z0 - x^87*y*z0^2 - x^88*y - x^87*z0^2 - x^88 - x^87*y - x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 - x^87 + x^85*y*z0 - x^85*z0^2 + x^84*y*z0^2 - x^84*y*z0 - x^83*y*z0^2 - x^85 + x^84*z0 - x^84 - x^83*y - x^82*z0^2 - x^83 + x^82*y - x^82*z0 + x^81*y*z0 + x^81*z0^2 - x^82 - x^81*y - x^80*y*z0 - x^79*y*z0^2 + x^80*y - x^79*y*z0 - x^80 + x^78*y*z0 + x^79 + x^78*y - x^78*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 - x^77*z0 - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y + x^75*y*z0 + x^75*z0^2 + x^76 - x^75*z0 + x^74*y*z0 - x^74*z0^2 - x^74*y - x^74*z0 - x^73*y*z0 + x^73*z0^2 - x^72*y*z0^2 + x^74 - x^73*y - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 - x^72 - x^71*y + x^71*z0 + x^69*y*z0^2 + x^70*y - x^70*z0 - x^69*y*z0 - x^68*y*z0^2 + x^69*z0 + x^68*y*z0 + x^68*z0^2 - x^67*y*z0^2 + x^68*y - x^68*z0 + x^67*z0^2 + x^68 + x^67*y + x^67*z0 + x^66*y - x^65*y*z0 + x^65*z0^2 + x^64*y*z0^2 + x^66 - x^65*z0 + x^64*y*z0 - x^65 + x^64*y + x^64*z0 + x^63*y*z0 + x^63*z0^2 + x^62*y*z0^2 - x^64 - x^63*y + x^63*z0 + x^61*y*z0^2 + x^62*y + x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 - x^60*y*z0 + x^61 + x^60*y - x^60*z0 + x^59*y*z0 + x^58*y*z0^2 - x^60 - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 - x^59 - x^57*y*z0 - x^57*z0^2 + x^58 + x^57*y + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56 - x^55*y + x^54*z0^2,
 -x^115 + x^114*z0 - x^113*z0^2 + x^113*z0 + x^113 + x^112*y - x^112*z0 - x^111*y*z0 + x^110*y*z0^2 + x^111*z0 - x^110*y*z0 + x^111 - x^110*y + x^110*z0 + x^109*y*z0 - x^109*z0^2 - x^110 - x^108*y*z0 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 + x^106*y*z0^2 - x^107*y + x^107*z0 - x^106*y*z0 + x^105*y*z0^2 - x^106*y - x^106*z0 - x^105*z0^2 + x^104*y*z0^2 - x^105*y - x^105*z0 - x^104*y*z0 - x^104*z0^2 - x^104*y - x^104*z0 + x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^103*y - x^102*y*z0 - x^101*y*z0^2 - x^103 + x^101*z0^2 + x^102 - x^101*y - x^101*z0 - x^100*y*z0 - x^101 - x^100*y + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^99*y + x^98*y*z0 + x^97*y*z0^2 - x^99 + x^98*y - x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^97*y - x^97*z0 + x^96*y*z0 + x^96*z0^2 + x^95*y*z0^2 + x^96*y + x^95*z0^2 + x^96 - x^94*y*z0 + x^94*z0^2 + x^93*y*z0^2 + x^94*y - x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*y - x^92*z0 + x^91*y*z0 + x^90*y*z0^2 + x^91*y - x^90*z0^2 - x^91 + x^90*y - x^90*z0 + x^88*y*z0^2 + x^89*y + x^89*z0 + x^88*y*z0 + x^87*y*z0^2 + x^88*y - x^88*z0 - x^87*z0^2 + x^86*y*z0^2 - x^88 + x^87*y - x^87*z0 - x^86*y*z0 + x^86*z0^2 - x^87 - x^86*y - x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^85*z0 + x^83*y*z0^2 - x^84*y + x^84*z0 - x^83*y*z0 + x^84 + x^83*z0 - x^81*y*z0^2 + x^82*z0 - x^81*y*z0 - x^81*z0^2 - x^80*y*z0^2 + x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 + x^79*y - x^78*y*z0 - x^78*z0^2 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 + x^78 - x^77*y - x^76*y*z0 - x^75*y*z0^2 - x^76*y + x^76*z0 + x^75*y*z0 - x^76 - x^75*z0 + x^74*y*z0 - x^73*y*z0^2 + x^75 + x^74*z0 + x^73*y*z0 - x^74 - x^73*y + x^73*z0 - x^72*z0^2 + x^71*y*z0^2 + x^73 - x^72*y - x^72*z0 - x^71*z0^2 - x^70*y*z0^2 - x^72 + x^71*y + x^71*z0 + x^70*y*z0 + x^69*y*z0^2 - x^71 - x^68*y*z0^2 + x^70 - x^69*y + x^69*z0 - x^68*y*z0 - x^68*z0^2 - x^67*y*z0^2 + x^69 - x^68*z0 - x^67*y*z0 + x^66*y*z0^2 - x^68 - x^67*y + x^66*z0^2 - x^65*y*z0^2 + x^67 + x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 + x^64*y*z0^2 + x^65*y + x^65*z0 + x^64*y*z0 - x^65 + x^64*y - x^64*z0 - x^63*y*z0 - x^62*y*z0^2 + x^63*z0 - x^62*y*z0 + x^62*z0^2 + x^61*y*z0^2 + x^63 + x^62*y - x^62*z0 - x^61*z0^2 + x^60*y*z0^2 + x^61*y + x^61*z0 - x^60*z0^2 + x^59*y*z0^2 - x^61 - x^60*y - x^59*y*z0 - x^59*z0^2 - x^60 + x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^57*y*z0 - x^57*z0^2 - x^58 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^55*y + x^54*y,
 x^115 + x^114*z0 + x^114 - x^112*z0^2 + x^113 - x^112*y - x^111*y*z0 - x^111*z0^2 - x^111*y + x^111*z0 + x^109*y*z0^2 + x^111 - x^110*y + x^110*z0 - x^109*z0^2 + x^108*y*z0^2 + x^110 - x^109*z0 - x^108*y*z0 + x^108*z0^2 - x^109 - x^108*y + x^108*z0 - x^107*y*z0 - x^107*z0^2 + x^106*y*z0^2 + x^107*y - x^105*y*z0^2 + x^107 - x^106*y + x^105*y*z0 - x^105*z0^2 - x^104*y*z0^2 - x^106 + x^105*y + x^105*z0 + x^104*z0^2 - x^103*y*z0^2 + x^104*y + x^104*z0 - x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 - x^103*z0 - x^102*z0^2 + x^103 + x^102*y + x^102*z0 - x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 + x^101*z0 + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*z0 + x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^97*y*z0^2 + x^99 - x^98*y - x^98*z0 - x^96*y*z0^2 - x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 + x^96*y + x^95*y*z0 - x^95*z0^2 + x^94*y*z0^2 - x^96 - x^95*y + x^94*y*z0 + x^93*y*z0^2 + x^94*z0 - x^93*y*z0 - x^93*z0^2 - x^92*y*z0^2 - x^94 + x^93*y - x^93*z0 - x^92*y*z0 + x^92*z0^2 + x^91*y*z0^2 - x^93 - x^92*z0 - x^91*y*z0 + x^90*y*z0^2 + x^90*y*z0 - x^90*z0^2 - x^89*y*z0^2 + x^90*y + x^90*z0 - x^89*y*z0 + x^88*y*z0^2 - x^90 - x^89*y + x^89*z0 + x^87*y*z0^2 + x^89 - x^88*y + x^88*z0 + x^87*z0^2 + x^88 + x^87*y - x^86*z0^2 - x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 - x^85*y*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 + x^85*y + x^85*z0 - x^84*z0^2 - x^83*y*z0^2 + x^85 + x^83*z0^2 - x^82*y*z0^2 - x^84 - x^82*y*z0 - x^82*z0^2 - x^81*y*z0^2 + x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^81*z0^2 + x^82 - x^81*y + x^80*y*z0 + x^79*y*z0^2 - x^81 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^80 - x^78*y*z0 - x^78*z0^2 + x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y - x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*z0^2 - x^76 + x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y - x^74*z0 + x^73*y*z0 - x^73*z0^2 - x^74 - x^73*y - x^73*z0 + x^72*y*z0 - x^72*z0^2 - x^71*y*z0^2 - x^73 + x^72*y + x^71*z0^2 - x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 - x^70*z0^2 - x^69*y*z0^2 - x^71 + x^70*z0 - x^69*y*z0 - x^69*z0^2 - x^70 + x^69*y - x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*y - x^67*y*z0 + x^68 + x^67*y + x^65*y*z0^2 - x^67 + x^66*y - x^66*z0 - x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^66 + x^65*y - x^64*y*z0 + x^64*z0^2 + x^63*y*z0^2 + x^64*y - x^63*y*z0 + x^63*z0^2 + x^64 - x^63*z0 + x^62*z0^2 - x^61*y*z0^2 + x^62*y + x^61*y*z0 + x^61*z0^2 - x^60*y*z0^2 - x^62 - x^61*y + x^61*z0 + x^60*y*z0 - x^60*z0^2 - x^59*y*z0^2 - x^61 + x^60*y - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 - x^59*y - x^59*z0 - x^58*y*z0 + x^58*z0^2 - x^57*y*z0^2 + x^59 + x^58*z0 - x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^57*z0 + x^55*y*z0^2 - x^57 - x^56*z0 + x^55*y*z0 - x^55*y + x^54*y*z0,
 -x^115 + x^113*z0^2 - x^114 - x^113*z0 + x^112*z0^2 + x^113 + x^112*y + x^112*z0 - x^111*z0^2 - x^110*y*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 - x^109*y*z0^2 + x^111 - x^110*y - x^109*y*z0 + x^109*z0^2 + x^108*y*z0^2 - x^110 + x^109*z0 - x^108*y*z0 + x^107*y*z0^2 - x^108*y + x^108*z0 - x^107*z0^2 - x^106*y*z0^2 - x^108 - x^107*y - x^107*z0 - x^106*y*z0 + x^106*z0^2 - x^105*y*z0^2 + x^107 - x^106*y - x^104*y*z0^2 + x^105*y + x^105*z0 + x^104*y*z0 - x^103*y*z0^2 + x^105 + x^104*y + x^103*y*z0 + x^103*z0^2 - x^102*y*z0^2 + x^104 - x^103*y - x^103*z0 + x^102*y*z0 - x^103 - x^102*y + x^102*z0 - x^101*y*z0 + x^101*z0^2 + x^100*y*z0^2 + x^102 - x^101*z0 - x^100*y*z0 + x^99*y*z0^2 - x^100*y - x^100*z0 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 - x^100 - x^99*y + x^99*z0 - x^98*y*z0 - x^98*z0^2 - x^97*y*z0^2 - x^98*y - x^98*z0 - x^97*z0^2 - x^96*y*z0^2 + x^98 + x^97*y + x^96*y*z0 - x^95*y*z0^2 - x^97 - x^96*y - x^96*z0 - x^95*z0^2 - x^94*y*z0^2 + x^95*y + x^95*z0 - x^94*y*z0 + x^94*z0^2 - x^95 - x^94*y + x^94 - x^93*y + x^93*z0 - x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 + x^93 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^91*y - x^91*z0 + x^90*y*z0 + x^91 + x^90*y - x^90*z0 + x^89*z0 - x^88*y*z0 - x^87*y*z0^2 + x^88*y - x^87*y*z0 - x^86*y*z0^2 + x^87*y + x^86*y*z0 - x^86*z0^2 - x^85*y*z0^2 + x^86*y + x^86*z0 - x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y - x^84*z0^2 - x^83*y*z0^2 - x^83*y*z0 + x^84 - x^83*z0 + x^82*y*z0 + x^82*z0^2 + x^81*y*z0^2 + x^83 + x^82*y + x^82*z0 + x^81*z0^2 - x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 - x^80*z0^2 + x^79*y*z0^2 - x^81 - x^79*y*z0 + x^79*z0^2 + x^78*y*z0^2 - x^79*y - x^79*z0 + x^78*y*z0 + x^77*y*z0^2 - x^79 - x^78*z0 - x^77*y*z0 - x^77*z0^2 + x^78 + x^76*y*z0 + x^76*z0^2 - x^77 + x^76*y + x^76*z0 - x^75*y*z0 - x^75*z0^2 + x^76 + x^75*z0 + x^74*z0^2 - x^75 - x^74*z0 - x^73*z0^2 - x^72*y*z0^2 + x^74 + x^73*y - x^73*z0 - x^72*y*z0 - x^71*y*z0^2 + x^73 + x^72*y - x^72*z0 - x^71*y*z0 + x^70*y*z0^2 - x^72 - x^71*z0 + x^70*y*z0 + x^70*z0^2 - x^71 + x^70*z0 - x^69*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^67*y*z0^2 - x^68*y + x^67*y*z0 + x^68 - x^67*z0 + x^66*z0^2 - x^65*y*z0^2 + x^67 - x^66*y + x^66*z0 + x^65*y*z0 - x^65*z0^2 - x^64*y*z0^2 - x^66 - x^65*y + x^65*z0 + x^64*z0^2 + x^63*y*z0^2 + x^65 - x^64*y - x^64*z0 - x^63*y*z0 + x^63*z0^2 - x^62*y*z0^2 + x^63*y - x^63*z0 + x^62*y*z0 - x^61*y*z0^2 - x^63 - x^62*y - x^61*y*z0 - x^61*z0^2 - x^61*y - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 - x^59*y + x^58*y*z0 - x^58*z0^2 + x^58*y - x^57*z0^2 - x^56*y*z0^2 + x^57*y - x^56*y*z0 - x^55*y*z0^2 - x^57 - x^56*y - x^56*z0 + x^55*y*z0 + x^54*y*z0^2 - x^56,
 -x^115 - x^114*z0 - x^114 - x^113*z0 - x^113 + x^112*y + x^112*z0 + x^111*y*z0 - x^111*z0^2 + x^111*y + x^111*z0 + x^110*y*z0 - x^110*z0^2 + x^111 + x^110*y - x^109*y*z0 + x^108*y*z0^2 + x^109*z0 - x^108*y*z0 - x^108*z0^2 + x^107*y*z0^2 - x^109 - x^108*y - x^107*z0^2 + x^107*y + x^106*z0^2 + x^105*y*z0^2 + x^106*z0 - x^105*y*z0 - x^105*z0^2 + x^104*y*z0^2 + x^106 - x^105*y - x^105*z0 - x^104*z0^2 - x^105 + x^104*y + x^104*z0 - x^103*z0^2 - x^104 + x^103*y + x^102*z0^2 - x^101*y*z0^2 - x^103 + x^102*z0 + x^101*y*z0 - x^101*z0^2 - x^100*y*z0^2 - x^101*y - x^100*y*z0 + x^99*y*z0^2 + x^101 - x^100*y - x^99*y*z0 + x^99*z0^2 + x^98*y*z0^2 + x^100 - x^99*z0 - x^98*y*z0 - x^98*z0^2 + x^98*y - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^97*z0 - x^96*y*z0 + x^97 + x^94*y*z0^2 + x^96 - x^95*y + x^94*z0^2 + x^93*y*z0^2 - x^95 + x^94*y - x^94*z0 - x^93*y*z0 - x^92*y*z0^2 - x^94 + x^93*y + x^93*z0 + x^92*y*z0 - x^92*z0^2 + x^91*y*z0^2 + x^92*y - x^92*z0 + x^91*y*z0 - x^90*y*z0^2 - x^92 - x^91*z0 + x^90*y*z0 - x^89*y*z0^2 + x^91 + x^90*z0 + x^88*y*z0^2 + x^89*y + x^89*z0 + x^87*y*z0^2 + x^89 + x^88*y - x^88*z0 + x^87*y*z0 - x^86*y*z0^2 - x^88 - x^87*y - x^87*z0 + x^86*y*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^86*y - x^86*z0 - x^85*z0^2 - x^84*y*z0^2 - x^86 - x^85*y - x^85*z0 - x^84*z0^2 - x^85 + x^84*z0 + x^83*z0^2 + x^84 + x^83*y + x^83*z0 + x^82*y + x^82*z0 + x^82 + x^81*z0 - x^80*z0^2 + x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 - x^79*y*z0 + x^79*y - x^79*z0 + x^78*y*z0 - x^77*y*z0^2 + x^79 - x^78*y + x^77*z0^2 + x^76*y*z0^2 + x^78 - x^77*y + x^76*y*z0 + x^77 - x^76*y - x^74*y*z0^2 + x^75*y + x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 - x^74*y + x^74*z0 - x^73*z0^2 + x^72*y*z0^2 + x^74 + x^73*y - x^72*z0^2 + x^71*y*z0^2 - x^73 + x^72*y + x^72*z0 - x^71*y*z0 + x^70*y*z0^2 + x^72 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 + x^71 + x^70*y - x^70*z0 - x^69*y*z0 + x^68*y*z0^2 + x^69*z0 - x^67*y*z0^2 + x^69 - x^68*z0 + x^68 - x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*z0 + x^65*y + x^65*z0 + x^64*y*z0 + x^64*z0^2 - x^65 + x^63*y*z0 - x^63*z0^2 - x^63*z0 - x^62*z0^2 - x^63 - x^61*y*z0 - x^61*z0^2 + x^60*y*z0^2 - x^61*z0 - x^60*y*z0 + x^60*z0^2 + x^59*y*z0^2 + x^60*y + x^59*y*z0 - x^59*z0^2 + x^58*y*z0^2 + x^60 + x^59*y + x^59*z0 + x^57*y*z0^2 - x^59 - x^58*z0 + x^57*y*z0 - x^57*z0^2 - x^56*y*z0^2 + x^58 + x^57*y - x^57*z0 - x^56*z0^2 - x^57 + x^56*y - x^56*z0 - x^55*y*z0 + x^56 - x^55*y + x^55,
 -x^114*z0 - x^113*z0^2 - x^112*z0^2 + x^112*z0 + x^111*y*z0 + x^111*z0^2 + x^110*y*z0^2 - x^112 - x^110*z0^2 + x^109*y*z0^2 + x^111 - x^109*y*z0 - x^108*y*z0^2 + x^110 + x^109*y - x^109*z0 + x^107*y*z0^2 - x^108*y - x^108*z0 + x^107*z0^2 - x^108 - x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^105*y*z0^2 - x^106*z0 - x^105*y*z0 + x^105*z0^2 + x^104*y*z0^2 - x^106 + x^105*y - x^105*z0 + x^104*y*z0 - x^103*y*z0^2 - x^105 + x^104*y + x^104*z0 - x^102*y*z0^2 + x^104 + x^103*y + x^102*y*z0 + x^102*z0^2 + x^101*y*z0^2 - x^103 - x^102*y + x^101*z0^2 + x^101*y - x^101*z0 - x^100*y*z0 + x^100*z0^2 + x^99*y*z0^2 - x^101 - x^100*y - x^100*z0 - x^99*z0^2 + x^100 + x^99*y - x^99*z0 + x^98*y*z0 + x^98*z0^2 - x^98*y - x^98*z0 + x^97*z0^2 + x^98 + x^97*y - x^97*z0 - x^96*y*z0 - x^97 - x^94*y*z0^2 - x^96 - x^95*y + x^95*z0 - x^94*z0^2 - x^95 - x^93*y*z0 - x^93*z0^2 + x^94 + x^93*y + x^92*y*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*z0 - x^91*z0^2 + x^90*y*z0^2 - x^92 - x^91*y + x^90*y*z0 + x^89*y*z0^2 - x^91 - x^90*y - x^90*z0 + x^89*y*z0 + x^89*z0^2 - x^88*y*z0^2 - x^90 + x^89*y - x^89 + x^88*y + x^88*z0 + x^87*z0^2 - x^86*y*z0^2 + x^87*z0 + x^86*z0^2 + x^85*y*z0^2 + x^87 + x^85*y*z0 + x^85*z0^2 + x^84*y*z0^2 + x^86 - x^85*y + x^85*z0 + x^84*y*z0 + x^84*z0^2 - x^83*y*z0^2 + x^84*z0 - x^83*y*z0 + x^84 + x^83*y - x^83*z0 - x^82*y*z0 + x^82*z0^2 - x^81*y*z0^2 - x^82*y - x^82*z0 + x^81*y*z0 - x^81*z0^2 + x^80*y*z0^2 - x^82 - x^81*y - x^81*z0 + x^80*y*z0 - x^79*y*z0^2 + x^81 - x^80*y + x^80*z0 + x^79*z0^2 + x^80 - x^79*z0 - x^78*y*z0 + x^77*y*z0^2 - x^78*y + x^78*z0 - x^77*y*z0 + x^77*z0^2 - x^76*y*z0^2 + x^78 + x^77*y + x^77*z0 - x^76*y*z0 + x^75*y*z0^2 + x^77 - x^76*y - x^75*y*z0 + x^74*y*z0^2 - x^76 - x^75*y - x^74*y*z0 + x^73*y*z0^2 + x^75 - x^74*y + x^74*z0 - x^73*y*z0 - x^73*z0^2 - x^72*y*z0^2 - x^73*y + x^73*z0 - x^72*y*z0 - x^72*z0^2 + x^71*y*z0^2 - x^72*y + x^71*y*z0 + x^71*z0^2 - x^70*y*z0^2 + x^71*y - x^70*y*z0 + x^70*z0^2 + x^69*y*z0^2 - x^71 + x^70*y + x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 + x^69*y - x^68*y*z0 + x^68*z0^2 + x^67*y*z0^2 - x^69 + x^68*z0 - x^67*y*z0 - x^67*z0^2 + x^66*y*z0^2 + x^68 + x^66*z0^2 + x^65*y*z0^2 - x^67 + x^66*y + x^65*y*z0 + x^65*z0^2 - x^64*y*z0^2 + x^65*y - x^65*z0 + x^63*y*z0^2 + x^65 + x^64*y - x^63*z0^2 + x^62*y*z0^2 + x^63*y - x^62*y*z0 - x^61*y*z0^2 + x^63 + x^60*y*z0^2 + x^62 - x^61*y + x^61*z0 - x^60*z0^2 + x^61 + x^60*y - x^60*z0 - x^59*y*z0 + x^59*z0^2 - x^58*y*z0^2 + x^60 + x^59*y - x^59*z0 + x^58*z0^2 + x^57*y*z0^2 + x^59 + x^58*y + x^58*z0 - x^57*z0^2 - x^58 + x^57*y + x^57*z0 - x^56*y*z0 + x^56*z0^2 + x^55*y*z0^2 - x^57 + x^56*y + x^56*z0 + x^55*y*z0 - x^56 + x^55*z0,
 x^114*z0 + x^113*z0^2 + x^114 - x^113*z0 - x^112*z0^2 - x^113 + x^112*z0 - x^111*y*z0 - x^110*y*z0^2 - x^112 - x^111*y - x^111*z0 + x^110*y*z0 + x^109*y*z0^2 - x^111 + x^110*y + x^110*z0 - x^109*y*z0 - x^109*z0^2 - x^110 + x^109*y + x^108*y*z0 - x^108*z0^2 + x^108*y - x^107*y*z0 + x^106*y*z0^2 + x^108 + x^107*y + x^107*z0 - x^106*y*z0 + x^106*z0^2 + x^107 - x^106*y + x^106*z0 - x^105*z0^2 - x^106 - x^105*y + x^105*z0 - x^104*y*z0 - x^104*z0^2 + x^104*y - x^104*z0 - x^103*y*z0 + x^103*z0^2 + x^102*y*z0^2 - x^104 - x^103*z0 - x^102*y*z0 - x^101*y*z0^2 - x^103 - x^102*y + x^100*y*z0^2 + x^102 - x^101*y + x^100*y*z0 + x^99*y*z0^2 + x^101 - x^99*y*z0 + x^99*z0^2 - x^98*y*z0^2 + x^100 + x^99*z0 + x^98*y*z0 + x^99 - x^98*y + x^97*y*z0 - x^97*z0^2 + x^96*y*z0^2 + x^98 + x^96*y*z0 - x^96*z0^2 - x^95*y*z0^2 + x^97 - x^96*y - x^96*z0 - x^95*z0^2 + x^94*y*z0^2 - x^95*y - x^94*z0^2 + x^93*y*z0^2 - x^94*z0 + x^93*y*z0 + x^93*y + x^93*z0 - x^92*z0^2 - x^91*y*z0^2 - x^92*z0 + x^91*y*z0 - x^91*z0^2 - x^90*y*z0^2 + x^92 + x^91*y - x^91*z0 - x^90*y*z0 + x^90*z0^2 - x^89*y*z0^2 + x^90*y - x^90*z0 - x^89*y*z0 - x^89*z0^2 + x^88*y*z0^2 + x^90 - x^89*y - x^88*z0^2 - x^87*y*z0^2 + x^89 + x^88*y + x^88*z0 + x^87*y*z0 - x^86*y*z0^2 + x^88 + x^87*z0 + x^87 - x^86*y - x^86*z0 - x^85*y*z0 + x^85*z0^2 - x^85*y - x^84*z0^2 + x^83*y*z0 - x^83*z0^2 - x^84 + x^83*z0 + x^82*y*z0 - x^83 - x^82*y - x^82*z0 - x^81*y*z0 - x^80*y*z0^2 - x^82 - x^81*y + x^80*y*z0 + x^80*z0^2 + x^79*y*z0^2 - x^80*y - x^80*z0 + x^79*y*z0 - x^79*z0^2 - x^78*y*z0^2 + x^79*y - x^77*y*z0^2 - x^78*z0 + x^77*y*z0 + x^76*y*z0^2 - x^78 - x^77*y - x^77*z0 + x^76*y*z0 + x^76*z0^2 - x^75*y*z0^2 - x^77 + x^76*y - x^75*y*z0 + x^74*y*z0^2 + x^76 - x^75*y - x^74*y*z0 - x^74*z0^2 - x^73*y*z0^2 + x^74*y - x^72*y*z0^2 - x^73*z0 + x^72*y*z0 + x^72*z0 - x^71*z0^2 - x^71*y - x^71*z0 - x^69*y*z0^2 - x^71 - x^70*y + x^70*z0 - x^69*y*z0 + x^69*z0^2 - x^68*y*z0^2 + x^70 - x^69*y - x^69*z0 + x^68*z0^2 - x^68*y + x^68*z0 + x^67*z0^2 - x^66*y*z0^2 + x^68 - x^67*y + x^67*z0 - x^66*z0^2 + x^65*y*z0^2 - x^67 - x^66*y + x^66*z0 - x^65*y*z0 + x^65*z0^2 + x^66 + x^65*y + x^65*z0 - x^64*y*z0 + x^64*z0 + x^63*y*z0 + x^62*y*z0^2 - x^63*y + x^62*y*z0 - x^61*y*z0^2 - x^63 + x^62*z0 - x^61*z0^2 - x^62 + x^61*y + x^60*z0^2 + x^61 + x^60*y + x^60*z0 - x^59*y*z0 + x^58*y*z0^2 - x^59*y - x^59*z0 + x^58*y*z0 - x^58*z0^2 + x^57*y*z0^2 - x^58*z0 - x^57*y*z0 - x^56*y*z0^2 + x^57*z0 - x^56*y*z0 + x^56*z0^2 - x^57 - x^56*z0 + x^55*z0^2 + x^56]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomrphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[((-x^2*z0 + y)/y) * dx,
 (1/y) * dx,
 (z0/y) * dx,
 (z0^2/y) * dx,
 (x/y) * dx,
 (x*z0/y) * dx,
 ((-x^3 + x*z0^2)/y) * dx,
 (x^2/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lpseud_magical_element(threshold = 30)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lAS.pseudo_magical_lment(threhold = 30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     if omega.valuation() < 0:

....:         print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7l....:         print(omega, omega.trace(), omega - omega.group_action([1]))

....: [?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     if omega.valuation() < 0:

....:         print(omega, omega.trace(), omega - omega.group_action([1]))

....: 

[?7h[?12l[?25h[?2004l((x^4 + x^2*z0^2 + y*z0)/y) * dx ((-x^2)/y) dx ((x^2*z0 - x^2 - y)/y) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lat_most_poles_orms(1)[?7h[?12l[?25h[?25l[?7lt_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: AS.at_most_poles_forms(1)

[?7h[?12l[?25h[?2004l[?7h[((-x^2*z0 + y)/y) * dx,
 ((x^4 + x^2*z0^2 + y*z0)/y) * dx,
 (1/y) * dx,
 (z0/y) * dx,
 (z0^2/y) * dx,
 (x/y) * dx,
 (x*z0/y) * dx,
 ((-x^3 + x*z0^2)/y) * dx,
 (x^2/y) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lsage: for omega in AS.at_most_poles_forms(1):

....:     if omega.valuation() < 0:

....:         print(omega, omega.trace(), omega - omega.group_action([1]))[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_form(1)

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1;3S[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
[?2004l
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Using Python 3.11.1. Type "help()" for help.                       │
│ Enhanced for CoCalc.                                               │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [2], line 1
----> 1 AS

NameError: name 'AS' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [C.y], prec = 200)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t^2 + 2*t^3 + t^8 + t^9 + 2*t^14 + 2*t^15 + t^17 + 2*t^18 + 2*t^20 + 2*t^24 + 2*t^26 + t^27 + 2*t^29 + t^35 + 2*t^42 + t^47 + 2*t^48 + 2*t^51 + 2*t^53 + t^54 + 2*t^56 + 2*t^60 + 2*t^62 + t^68 + 2*t^74 + t^78 + t^81 + 2*t^83 + 2*t^87 + t^89 + 2*t^93 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-1 + t^4 + t^5 + t^9 + t^10 + 2*t^14 + t^15 + t^17 + t^19 + 2*t^23 + 2*t^25 + 2*t^27 + t^28 + t^30 + 2*t^32 + t^34 + t^41 + 2*t^43 + 2*t^44 + 2*t^45 + t^49 + 2*t^50 + t^53 + 2*t^54 + t^55 + t^63 + 2*t^69 + 2*t^71 + t^73 + 2*t^75 + 2*t^77 + t^81 + t^82 + t^84 + 2*t^90 + t^94 + 2*t^98 + O(t^99)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(place = 1)

[?7h[?12l[?25h[?2004l[?7h2*t^-1 + t^4 + 2*t^5 + 2*t^9 + t^10 + 2*t^14 + 2*t^15 + 2*t^17 + 2*t^19 + t^23 + t^25 + t^27 + t^28 + t^30 + 2*t^32 + t^34 + 2*t^41 + t^43 + 2*t^44 + t^45 + 2*t^49 + 2*t^50 + 2*t^53 + 2*t^54 + 2*t^55 + 2*t^63 + t^69 + t^71 + 2*t^73 + t^75 + t^77 + 2*t^81 + t^82 + t^84 + 2*t^90 + t^94 + 2*t^98 + O(t^99)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7l= AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles_forms(1)[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = AS.at_most_poles_forms(1)[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega.expansion

 omega.expansion         

 omega.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 omega.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 omega.expansion         

 omega.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(





[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 0)

[?7h[?12l[?25h[?2004l[?7ht^-1 + t + t^3 + t^5 + t^7 + t^9 + 2*t^10 + 2*t^12 + t^13 + t^14 + 2*t^15 + t^16 + t^18 + 2*t^19 + 2*t^20 + t^21 + 2*t^22 + t^23 + t^24 + t^25 + t^27 + t^31 + 2*t^33 + 2*t^35 + 2*t^36 + 2*t^37 + 2*t^38 + t^39 + t^40 + t^42 + t^44 + t^45 + t^46 + t^47 + t^48 + t^49 + t^50 + t^51 + 2*t^52 + 2*t^53 + 2*t^55 + 2*t^56 + t^57 + 2*t^59 + t^60 + 2*t^61 + 2*t^62 + t^63 + t^64 + t^66 + 2*t^67 + t^68 + t^69 + t^71 + 2*t^72 + t^73 + t^74 + 2*t^76 + t^77 + 2*t^78 + 2*t^79 + t^81 + t^82 + t^84 + t^85 + t^86 + 2*t^87 + t^88 + 2*t^89 + 2*t^91 + t^92 + t^93 + t^94 + 2*t^95 + 2*t^96 + 2*t^97 + t^99 + 2*t^100 + t^101 + t^102 + 2*t^104 + t^105 + 2*t^106 + t^107 + t^108 + t^110 + 2*t^111 + 2*t^113 + 2*t^114 + 2*t^115 + 2*t^116 + 2*t^117 + 2*t^120 + 2*t^122 + 2*t^123 + t^125 + 2*t^126 + 2*t^127 + 2*t^129 + t^131 + t^134 + t^136 + t^139 + t^141 + 2*t^142 + 2*t^143 + 2*t^144 + t^145 + t^146 + 2*t^147 + 2*t^148 + t^149 + 2*t^150 + 2*t^154 + t^156 + t^157 + 2*t^159 + t^160 + t^161 + 2*t^162 + 2*t^165 + 2*t^167 + 2*t^169 + 2*t^170 + 2*t^171 + 2*t^172 + t^175 + 2*t^177 + 2*t^180 + t^181 + 2*t^182 + t^183 + t^184 + t^186 + t^187 + 2*t^188 + t^189 + t^192 + t^193 + O(t^195)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 1)

[?7h[?12l[?25h[?2004l[?7h2*t^-1 + 2*t + 2*t^3 + 2*t^5 + 2*t^7 + 2*t^9 + 2*t^10 + 2*t^12 + 2*t^13 + t^14 + t^15 + t^16 + t^18 + t^19 + 2*t^20 + 2*t^21 + 2*t^22 + 2*t^23 + t^24 + 2*t^25 + 2*t^27 + 2*t^31 + t^33 + t^35 + 2*t^36 + t^37 + 2*t^38 + 2*t^39 + t^40 + t^42 + t^44 + 2*t^45 + t^46 + 2*t^47 + t^48 + 2*t^49 + t^50 + 2*t^51 + 2*t^52 + t^53 + t^55 + 2*t^56 + 2*t^57 + t^59 + t^60 + t^61 + 2*t^62 + 2*t^63 + t^64 + t^66 + t^67 + t^68 + 2*t^69 + 2*t^71 + 2*t^72 + 2*t^73 + t^74 + 2*t^76 + 2*t^77 + 2*t^78 + t^79 + 2*t^81 + t^82 + t^84 + 2*t^85 + t^86 + t^87 + t^88 + t^89 + t^91 + t^92 + 2*t^93 + t^94 + t^95 + 2*t^96 + t^97 + 2*t^99 + 2*t^100 + 2*t^101 + t^102 + 2*t^104 + 2*t^105 + 2*t^106 + 2*t^107 + t^108 + t^110 + t^111 + t^113 + 2*t^114 + t^115 + 2*t^116 + t^117 + 2*t^120 + 2*t^122 + t^123 + 2*t^125 + 2*t^126 + t^127 + t^129 + 2*t^131 + t^134 + t^136 + 2*t^139 + 2*t^141 + 2*t^142 + t^143 + 2*t^144 + 2*t^145 + t^146 + t^147 + 2*t^148 + 2*t^149 + 2*t^150 + 2*t^154 + t^156 + 2*t^157 + t^159 + t^160 + 2*t^161 + 2*t^162 + t^165 + t^167 + t^169 + 2*t^170 + t^171 + 2*t^172 + 2*t^175 + t^177 + 2*t^180 + 2*t^181 + 2*t^182 + 2*t^183 + t^184 + t^186 + 2*t^187 + 2*t^188 + 2*t^189 + t^192 + 2*t^193 + O(t^195)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)

[?7h[?12l[?25h[?2004l[?7ht^10 + t^12 + 2*t^14 + 2*t^16 + 2*t^18 + t^20 + t^22 + 2*t^24 + t^36 + t^38 + 2*t^40 + 2*t^42 + 2*t^44 + 2*t^46 + 2*t^48 + 2*t^50 + t^52 + t^56 + 2*t^60 + t^62 + 2*t^64 + 2*t^66 + 2*t^68 + t^72 + 2*t^74 + t^76 + t^78 + 2*t^82 + 2*t^84 + 2*t^86 + 2*t^88 + 2*t^92 + 2*t^94 + t^96 + t^100 + 2*t^102 + t^104 + t^106 + 2*t^108 + 2*t^110 + t^114 + t^116 + t^120 + t^122 + t^126 + 2*t^134 + 2*t^136 + t^142 + t^144 + 2*t^146 + t^148 + t^150 + t^154 + 2*t^156 + 2*t^160 + t^162 + t^170 + t^172 + t^180 + t^182 + 2*t^184 + 2*t^186 + t^188 + 2*t^192 + O(t^195)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l(1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l = AS.at_mospoles_forms(1)[1][?7h[?12l[?25h[?25l[?7lC.x.expansionat_infty(place = )[?7h[?12l[?25h[?25l[?7lomega = AS.atmost_poles_forms()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: omega = AS.at_most_poles_forms(1)[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = AS.at_most_poles_forms(1)[0][?7h[?12l[?25h[?25l[?7l.expansion_ainfty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lsage: omega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)

[?7h[?12l[?25h[?2004l[?7h2*t^15 + t^21 + 2*t^41 + t^47 + t^51 + 2*t^57 + t^59 + 2*t^65 + 2*t^69 + 2*t^75 + 2*t^77 + t^93 + t^95 + t^99 + t^101 + 2*t^103 + t^105 + 2*t^117 + 2*t^123 + 2*t^125 + 2*t^127 + 2*t^137 + t^139 + t^141 + t^143 + t^145 + t^149 + t^155 + t^157 + 2*t^159 + t^165 + 2*t^167 + t^171 + t^173 + 2*t^177 + t^179 + t^181 + t^183 + t^185 + t^191 + 2*t^193 + t^195 + 2*t^197 + O(t^198)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ loasage
[?2004l
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11                     │
│ Using Python 3.11.1. Type "help()" for help.                       │
│ Enhanced for CoCalc.                                               │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llambdaa = (v1-v0)/(u0 - u1)[?7h[?12l[?25h[?25l[?7load('init.sage'[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^4*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^5*z0 + x^4*z0 + x^2*z1) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^11 + x^9) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^11*z0 + x^9*z0 + x^8 + x^5*z1) * dx, z0*z1/x ), ( (x^10 + x^8) * dx, z1/x^2 ), ( (x^4) * dx, z0/x^2 ), ( (x^10*z0 + x^8*z0 + x^4*z1) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (0) * dx, z0/x^3 ), ( (x^9*z0 + x^7*z0 + x^3*z1) * dx, z0*z1/x^3 ), ( (x^8 + x^6) * dx, z1/x^4 ), ( (x^8*z0 + x^6*z0 + x^2*z1) * dx, z0*z1/x^4 ), ( (x^7*z0 + x^5*z0 + x^4*z0) * dx, z0*z1/x^5 ), ( (x^6*z0 + x^4*z0 + z1) * dx, z0*z1/x^6 ), ( (x^5*z0) * dx, z0*z1/x^7 ), ( (x^4*z0) * dx, z0*z1/x^8 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = x^13 + x^11

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lat_most_poles_superelliptic(C, 1)[?7h[?12l[?25h[?25l[?7llpha[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7lsage: alpha = C.x^((M - m)/2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega.expansion_at_infty(place = 0) + omega.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = AS.at_mospoles_forms(1)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l.y0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l.z0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l]0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[0*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*x^4*C.dx[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lCx^4*C.dx[?7h[?12l[?25h[?25l[?7l.x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega = C.z[0]*C.x^4*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor omega in AS.at_most_poles_forms(1):[?7h[?12l[?25h[?25l[?7l =x^3 -x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7l = C.z[1]/C.x^7[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0*z[1]/C.x^5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.z[1]/C.x^5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lift_to_de_rham[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.z[0]*C.x^4*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega + f.difn()[?7h[?12l[?25h[?25l[?7lmomega + f.difn()[?7h[?12l[?25h[?25l[?7l1omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7l=omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7lsage: om1 = omega + ff.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.valuation()

[?7h[?12l[?25h[?2004l[?7h14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h((x^13*z0 + x^11*z0 + x^10*z0 + x^10*z1 + x^8*z1 + x^7*z1 + z0*z1)/(x^12 + x^8 + x^6)) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7l = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz0*z1)/(x^12 + x^8 + x^6)) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( z0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7lCz0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.z0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCz1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.z1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1)/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l])/(x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.x^12 + x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l.x^8 + x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^6) * dx[?7h[?12l[?25h[?25l[?7l.x^6) * dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6)) * C.dx

[?7h[?12l[?25h[?2004l  Cell In [10], line 1
    om1 -(C.z[Integer(0)]*C.z[Integer(1)])/(C.x**Integer(12) + C.x**Integer(8) + C.x**Integer(6))) * C.dx
                                                                                                 ^
SyntaxError: unmatched ')'

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6)) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() * C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx

[?7h[?12l[?25h[?2004l[?7h((x^4*z0 + x*z1)/(x^3 + x + 1)) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7lsage: om2 = om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx\

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx\[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1-(C.z[0]*C.z[1])/(C.x^12 + C.x^8+ C.x^6) * C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 = om1 -(C.z[0]*C.z[1])/(C.x^12 + C.x^8 + C.x^6) * C.dx\[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2.valuation()

[?7h[?12l[?25h[?2004l[?7h14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lz[1].valuation()[?7h[?12l[?25h[?25l[?7l[1].valuation()[?7h[?12l[?25h[?25l[?7lsage: C.z[1].valuation()

[?7h[?12l[?25h[?2004l[?7h-26
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[1].valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].valuation()[?7h[?12l[?25h[?25l[?7l0].valuation()[?7h[?12l[?25h[?25l[?7lsage: C.z[0].valuation()

[?7h[?12l[?25h[?2004l[?7h-14
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l*C.genus()[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: 2*M - 3*m

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [17], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:33

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31

File <string>:390, in de_rham_basis(self, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [18], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:33

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31

File <string>:390, in de_rham_basis(self, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [19], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:33

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31

File <string>:390, in de_rham_basis(self, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [20], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:33

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31

File <string>:393, in de_rham_basis(self, threshold)

File <string>:372, in lift_to_de_rham(self, fct, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lI haven't found all forms, only  16  of  17
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [21], line 1
----> 1 load('init.sage')

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:33

File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:31

File <string>:393, in de_rham_basis(self, threshold)

File <string>:372, in lift_to_de_rham(self, fct, threshold)

File <string>:147, in holomorphic_differentials_basis(self, threshold)

NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0].valuation()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^5*z0 + x^4*z1 + x^2*z1) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4*z0 + x^3*z1) * dx, 0 ), ( (x^5*z0 + x^4*z1 + x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^8) * dx, 0 ), ( (x^11) * dx, z1/x ), ( (x^9) * dx, z0/x ), ( (x^11*z0 + x^10 + x^9*z1 + x^7*z0) * dx, z0*z1/x ), ( (x^10 + x^6) * dx, z1/x^2 ), ( (x^8) * dx, z0/x^2 ), ( (x^10*z0 + x^8*z1 + x^6*z0) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (0) * dx, z0/x^3 ), ( (x^9*z0 + x^7*z1 + x^5*z0) * dx, z0*z1/x^3 ), ( (x^8 + x^4) * dx, z1/x^4 ), ( (x^6) * dx, z0/x^4 ), ( (x^8*z0 + x^6*z1 + x^4*z0) * dx, z0*z1/x^4 ), ( (x^7*z0 + x^5*z0 + x^5*z1 + x^4*z1) * dx, z0*z1/x^5 ), ( (x^6*z0 + x^4*z1 + x^2*z0) * dx, z0*z1/x^6 ), ( (x^5*z0 + x^4*z0) * dx, z0*z1/x^7 ), ( (x^4*z0 + x^2*z1 + z0) * dx, z0*z1/x^8 ), ( (x^5*z0 + x^4*z1) * dx, z0*z1/x^9 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: i = 3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = p1*x + p0[?7h[?12l[?25h[?25l[?7lrint(licz)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.z[0].valuation()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^13 + x^9

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalpha = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lha = C.x^((M - m)/2)[?7h[?12l[?25h[?25l[?7lsage: alpha = C.x^((M - m)/2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = p1*x + p0[?7h[?12l[?25h[?25l[?7lrint(licz)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: prim = C.x^12 + C.x^8 + alpha*C.x^10

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega = C.z[0]*C.x^4*C.dx[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.x^4*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7li*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega = C.z[0]*C.x^i*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = C.z[0]*C.z[1]*C.x^4/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7li/(C.x^12 + C.x^10 + alpha*C.x^6)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: ff = C.z[0]*C.z[1]*C.x^i/prim

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.z[0]*C.x^i*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega + f.difn()[?7h[?12l[?25h[?25l[?7lmomega + f.difn()[?7h[?12l[?25h[?25l[?7l1omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7l=omega + f.difn()[?7h[?12l[?25h[?25l[?7l omega + f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = omega + ff.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7luation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.valuation()

[?7h[?12l[?25h[?2004l[?7h10
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.valuation()[?7h[?12l[?25h[?25l[?7l = omega + ff.diffn()[?7h[?12l[?25h[?25l[?7lff = C.z[0]*C.z[1]*C.x^i/prim[?7h[?12l[?25h[?25l[?7lomega = C.z[0]*C.x^i*C.dx[?7h[?12l[?25h[?25l[?7lprim = C.x^12 + C.x^8 + alpha*C.x^10[?7h[?12l[?25h[?25l[?7lalpha = C.x^((M- m)/2)[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7li = 3[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l2*M - 3*m[?7h[?12l[?25h[?25l[?7lC.z[0].valuation()[?7h[?12l[?25h[?25l[?7l2*M - 3*m[?7h[?12l[?25h[?25l[?7lsage: 2*M - 3*m

[?7h[?12l[?25h[?2004l[?7h-7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
[?2004l
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.0, Release Date: 2023-05-20                    │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll = 5[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = RA.gens()[?7h[?12l[?25h[?25l[?7lS = as_cover(C, [C.y], prec = 200)[?7h[?12l[?25h[?25l[?7l.at_most_poles_forms(1)[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
[?2004l
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.0, Release Date: 2023-05-20                    │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^5*z0 + x^2*z1) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^6*z0 + x^3*z1) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^8) * dx, 0 ), ( (x^13) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^13*z0 + x^10 + x^7*z1) * dx, z0*z1/x ), ( (x^12) * dx, z1/x^2 ), ( (x^6) * dx, z0/x^2 ), ( (x^12*z0 + x^6*z1) * dx, z0*z1/x^2 ), ( (x^11) * dx, z1/x^3 ), ( (0) * dx, z0/x^3 ), ( (x^11*z0 + x^5*z1) * dx, z0*z1/x^3 ), ( (x^10) * dx, z1/x^4 ), ( (x^4) * dx, z0/x^4 ), ( (x^10*z0 + x^4*z1) * dx, z0*z1/x^4 ), ( (x^9) * dx, z1/x^5 ), ( (x^9*z0 + x^6*z0) * dx, z0*z1/x^5 ), ( (x^8*z0 + x^2*z1) * dx, z0*z1/x^6 ), ( (x^7*z0) * dx, z0*z1/x^7 ), ( (x^6*z0 + z1) * dx, z0*z1/x^8 ), ( (x^5*z0) * dx, z0*z1/x^9 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h18
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1 = a_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l as_cover(C1, [C1.x^2, C1.x^5], prec = 300)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7l], prec = 30)[?7h[?12l[?25h[?25l[?7lx], prec = 30)[?7h[?12l[?25h[?25l[?7l^], prec = 30)[?7h[?12l[?25h[?25l[?7l3], prec = 30)[?7h[?12l[?25h[?25l[?7l3], prec = 30)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x^3], prec = 30)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, [C.x^3], prec = 30)[?7h[?12l[?25h[?25l[?7lsage: AS1 = as_cover(C, [C.x^33], prec = 300)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1 = as_cover(C, [C.x^33], prec = 300)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.genus()

[?7h[?12l[?25h[?2004l[?7h16
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
[?2004l
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.0, Release Date: 2023-05-20                    │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l18
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l18
16
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l18
16
7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.z[0].valuation()[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: C1.x.expansion

 C1.x.expansion         

 C1.x.expansion_at_infty





 [?7h[?12l[?25h[?25l[?7l

 C1.x.expansion         



 <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

 C1.x.expansion         

 C1.x.expansion_at_infty[?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-3 + O(t^97)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lAS1.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different

 AS2.exponent_of_different     

 AS2.exponent_of_different_prim

 



 [?7h[?12l[?25h[?25l[?7l(



[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS2.exponent_of_different()

[?7h[?12l[?25h[?2004l[?7h16
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lAS2.exponent_of_different()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS2.genus()

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l18
16
9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in product(*pr):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrang[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l18
16
9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = 13[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: a = 3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbeta = 1 + B[0]*t + B[1]*t^2 + B[2]*t^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: b = 5

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconj(pi)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: c = 11

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a+6*c > 6*b - 11[?7h[?12l[?25h[?25l[?7lsage: 3*a+6*c > 6*b - 11

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(2, 15):

....:     for b in range(2, 15):

....:         for c in range(2, 15):

....:             if a%2 == 1 and b%2 == 1 and c%1 == 1 and a != b and a != c:

....:                 if 3*a+6*c > 6*b - 11:

....:                     print(a, b, c)[?7h[?12l[?25h[?25l[?7l....:                     print(a, b, c)

....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(2, 15):

....:     for b in range(2, 15):

....:         for c in range(2, 15):

....:             if a%2 == 1 and b%2 == 1 and c%1 == 1 and a != b and a != c:

....:                 if 3*a+6*c > 6*b - 11:

....:                     print(a, b, c)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(2, 15):

....:     for b in range(2, 15):

....:         for c in range(2, 15):

....:             if a%2 == 1 and b%2 == 1 and c%1 == 1 and a != b and a != c:

....:                 if 3*a+6*c > 6*b - 11:

....:                     print(a, b, c)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a+6*c > 6*b - 11

 

 

 

 

 [?7h[?12l[?25h[?25l[?7lc = 11[?7h[?12l[?25h[?25l[?7lb5[?7h[?12l[?25h[?25l[?7la3[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l18
16
9
3 5 5
3 5 7
3 5 9
3 5 11
3 5 13
3 7 5
3 7 7
3 7 9
3 7 11
3 7 13
3 9 7
3 9 9
3 9 11
3 9 13
3 11 9
3 11 11
3 11 13
3 13 11
3 13 13
5 3 3
5 3 7
5 3 9
5 3 11
5 3 13
5 7 3
5 7 7
5 7 9
5 7 11
5 7 13
5 9 7
5 9 9
5 9 11
5 9 13
5 11 7
5 11 9
5 11 11
5 11 13
5 13 9
5 13 11
5 13 13
7 3 3
7 3 5
7 3 9
7 3 11
7 3 13
7 5 3
7 5 5
7 5 9
7 5 11
7 5 13
7 9 5
7 9 9
7 9 11
7 9 13
7 11 9
7 11 11
7 11 13
7 13 9
7 13 11
7 13 13
9 3 3
9 3 5
9 3 7
9 3 11
9 3 13
9 5 3
9 5 5
9 5 7
9 5 11
9 5 13
9 7 3
9 7 5
9 7 7
9 7 11
9 7 13
9 11 5
9 11 7
9 11 11
9 11 13
9 13 7
9 13 11
9 13 13
11 3 3
11 3 5
11 3 7
11 3 9
11 3 13
11 5 3
11 5 5
11 5 7
11 5 9
11 5 13
11 7 3
11 7 5
11 7 7
11 7 9
11 7 13
11 9 3
11 9 5
11 9 7
11 9 9
11 9 13
11 13 7
11 13 9
11 13 13
13 3 3
13 3 5
13 3 7
13 3 9
13 3 11
13 5 3
13 5 5
13 5 7
13 5 9
13 5 11
13 7 3
13 7 5
13 7 7
13 7 9
13 7 11
13 9 3
13 9 5
13 9 7
13 9 9
13 9 11
13 11 3
13 11 5
13 11 7
13 11 9
13 11 11
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ [?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ [?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
[?2004l
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.1, Release Date: 2023-08-20                    │
│ Create a "Sage Worksheet" file for the notebook interface.         │
│ Enhanced for CoCalc.                                               │
│ Using Python 3.11.1. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llambd = 1-z[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  8 -th root; divide by 2
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [1], line 1
----> 1 load('init.sage')

File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:8

File <string>:45, in __init__(self, C, list_of_fcts, branch_points, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [2], line 1
----> 1 load('init.sage')

File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:8

File <string>:75, in __truediv__(self, other)

File /ext/sage/10.1/src/sage/structure/element.pyx:488, in sage.structure.element.Element.__getattr__()
    486         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    487     """
--> 488     return self.getattr_from_category(name)
    489 
    490 cdef getattr_from_category(self, name):

File /ext/sage/10.1/src/sage/structure/element.pyx:501, in sage.structure.element.Element.getattr_from_category()
    499     else:
    500         cls = P._abstract_element_class
--> 501     return getattr_from_other_class(self, cls, name)
    502 
    503 def __dir__(self):

File /ext/sage/10.1/src/sage/cpython/getattr.pyx:362, in sage.cpython.getattr.getattr_from_other_class()
    360     dummy_error_message.cls = type(self)
    361     dummy_error_message.name = name
--> 362     raise AttributeError(dummy_error_message)
    363 attribute = <object>attr
    364 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [3], line 1
----> 1 load('init.sage')

File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:32

File /ext/sage/10.1/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
    173 
    174     if sage.repl.load.is_loadable_filename(filename):
--> 175         sage.repl.load.load(filename, globals())
    176         return
    177 

File /ext/sage/10.1/src/sage/repl/load.py:272, in load(filename, globals, attach)
    270             add_attached_file(fpath)
    271         with open(fpath) as f:
--> 272             exec(preparse_file(f.read()) + "\n", globals)
    273 elif ext == '.spyx' or ext == '.pyx':
    274     if attach:

File <string>:8

File <string>:75, in __truediv__(self, other)

File /ext/sage/10.1/src/sage/structure/element.pyx:488, in sage.structure.element.Element.__getattr__()
    486         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    487     """
--> 488     return self.getattr_from_category(name)
    489 
    490 cdef getattr_from_category(self, name):

File /ext/sage/10.1/src/sage/structure/element.pyx:501, in sage.structure.element.Element.getattr_from_category()
    499     else:
    500         cls = P._abstract_element_class
--> 501     return getattr_from_other_class(self, cls, name)
    502 
    503 def __dir__(self):

File /ext/sage/10.1/src/sage/cpython/getattr.pyx:362, in sage.cpython.getattr.getattr_from_other_class()
    360     dummy_error_message.cls = type(self)
    361     dummy_error_message.name = name
--> 362     raise AttributeError(dummy_error_message)
    363 attribute = <object>attr
    364 # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.elements()[?7h[?12l[?25h[?25l[?7lS2.genus()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (z0^2) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (-x*z0) * dx, z0^2/x ),
 ( (x*z0^2) * dx, z0^3/x ),
 ( (-2*x*z0^3) * dx, z0^4/x ),
 ( (-2*z0^3) * dx, z0^4/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: AS1

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
 z^5 - z = x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.holomorphic_diffentials()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In [7], line 1
----> 1 AS1.holomorphic_diffentials()

AttributeError: 'as_cover' object has no attribute 'holomorphic_diffentials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1.holomorphic_diffentials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_diffentials()[?7h[?12l[?25h[?25l[?7lsage: AS1.holomorphic_diffentials()

  AS1.a_number                            AS1.branch_points                       AS1.de_rham_basis                        

  AS1.at_most_poles                       AS1.cartier_matrix                      AS1.dx                                   

  AS1.at_most_poles_forms                 AS1.characteristic                      AS1.dx_series                           >

  AS1.base_ring                           AS1.cohomology_of_structure_sheaf_basis AS1.exponent_of_different                

 [?7h[?12l[?25h[?25l[?7la_number

 AS1.a_number                           







 <unknown> [?7h[?12l[?25h[?25l[?7lbranch_points

 AS1.a_number                            AS1.branch_points                      [?7h[?12l[?25h[?25l[?7lde_rham_basi

 AS1.branch_points                       AS1.de_rham_basis                      [?7h[?12l[?25h[?25l[?7lexponent_of_different_prim

 branch_pointsde_rham_basiexponent_of_different_prim

 cartiermatrixdx            fct_field

<characeristic     dx_seris     function

 cohomoloy_of_structure_sheaf_basisexpnent_of_different              genus                [?7h[?12l[?25h[?25l[?7lgroup

de_rham_basiexponent_of_different_primgroup                     

dx            fct_fieldheight   

dx_seris     functionholomorphic_differentials_basis

expnent_of_different              genus                ith_ramification_gp[?7h[?12l[?25h[?25l[?7ljumps

exponent_of_different_primgroup                     jumps

fct_fieldheight   lift_o_de_rham

functionholomorphic_differentials_basismagical_element                

genus                ith_ramification_gpnb_of_pts_at_nfty [?7h[?12l[?25h[?25l[?7lone

group                     jumpsone  

height   lift_o_de_rhamprec           

holomorphic_differentials_basismagical_element                pseudo_magical_element

ith_ramification_gpnb_of_pts_at_nfty quotien          [?7h[?12l[?25h[?25l[?7lramification_jumps

jumpsone  ramification_jumps

lift_o_de_rhamprec           uniformizer

magical_element                pseudo_magical_elementx                     

nb_of_pts_at_nfty quotien          x_series[?7h[?12l[?25h[?25l[?7ly

one  ramification_jumpsy                  

prec           uniformizery_series    

pseudo_magical_elementx                     z 

quotien          x_seriesz [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lramification_jumps

 AS1.ramification_jumps                  AS1.y                                  [?7h[?12l[?25h[?25l[?7lone

 AS1.one                                 AS1.ramification_jumps                 [?7h[?12l[?25h[?25l[?7ljumps

jumpsone               ramification_jumps 

lift_to_de_rhamprec       uniformizer 

magical_element       pseudo_magical_elementx>

nb_of_ps_at_inftyquotientx [?7h[?12l[?25h[?25l[?7lgroup

groupjumpsone               

heigh         lift_to_de_rhamprec       

holomorphic_differentials_basismagical_element       pseudo_magical_element

ith_ramificaton_gpnb_of_ps_at_inftyquotient[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim

exponent_of_different_primgroupjumps

fct_fieldheigh         lift_to_de_rham

functions                      holomorphic_differentials_basismagical_element       

genus              ith_ramificaton_gpnb_of_ps_at_infty[?7h[?12l[?25h[?25l[?7lde_rham_basis

de_rham_basis             exponent_of_different_primgroup

dx       fct_fieldheigh         

dx_seriefunctions                      holomorphic_differentials_basis

exponent_of_differentgenus              ith_ramificaton_gp[?7h[?12l[?25h[?25l[?7lbranch_point

branch_pointde_rham_basis             exponent_of_different_prim

cartier_matrixdx       fct_field

charactristicdx_seriefunctions                      

cohmology_of_structure_sheaf_basisexponent_of_differentgenus              [?7h[?12l[?25h[?25l[?7la_number

 a_number     branch_pointde_rham_basis             

 at_mostpoles cartier_matrixdx       

 at_mos_poles_formscharactristicdx_serie

 base_rin                          cohmology_of_structure_sheaf_basisexponent_of_different[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_diffentials()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l

 AS1.base_ring    

 AS1.branch_points[?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7lholomorphic_diffentials()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS1.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (z0) * dx, (z0^2) * dx, (x) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lfor d in range(1, 6):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l range(1, 6):[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lA = [[] for i in range(n)][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lC])[?7h[?12l[?25h[?25l[?7l.])[?7h[?12l[?25h[?25l[?7lx])[?7h[?12l[?25h[?25l[?7l^])[?7h[?12l[?25h[?25l[?7ld])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lA = [[] for i in range(n)][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for d in range(1, 6):

....:     AS = as_cover(C, [C.x^d])

....:     AS.holomorphic_differentials_basis()

....: 

[?7h[?12l[?25h[?2004l[?7h[]
[?7h[(1) * dx, (z0) * dx]
Increase precision.
[?7h[(1) * dx,
 (z0) * dx,
 (z0^2) * dx,
 (z0^3) * dx,
 (z0^4) * dx,
 (x) * dx,
 (x*z0) * dx,
 (x*z0^2) * dx,
 (x*z0^3) * dx,
 (x*z0^4) * dx,
 (x^2) * dx,
 (x^2*z0) * dx,
 (x^2*z0^2) * dx,
 (x^2*z0^3) * dx,
 (x^2*z0^4) * dx,
 (x^3) * dx,
 (x^3*z0) * dx,
 (x^3*z0^2) * dx,
 (x^3*z0^3) * dx,
 (x^3*z0^4) * dx,
 (x^4) * dx,
 (x^4*z0) * dx,
 (x^4*z0^2) * dx,
 (x^4*z0^3) * dx,
 (x^4*z0^4) * dx,
 (x^5) * dx,
 (x^5*z0) * dx,
 (x^5*z0^2) * dx,
 (x^5*z0^3) * dx,
 (x^5*z0^4) * dx,
 (x^6) * dx,
 (x^6*z0) * dx,
 (x^6*z0^2) * dx,
 (x^6*z0^3) * dx,
 (x^6*z0^4) * dx,
 (x^7) * dx,
 (x^7*z0) * dx,
 (x^7*z0^2) * dx,
 (x^7*z0^3) * dx,
 (x^7*z0^4) * dx]
Increase precision.
[?7h[(1) * dx,
 (z0) * dx,
 (z0^2) * dx,
 (z0^3) * dx,
 (z0^4) * dx,
 (x) * dx,
 (x*z0) * dx,
 (x*z0^2) * dx,
 (x*z0^3) * dx,
 (x*z0^4) * dx,
 (x^2) * dx,
 (x^2*z0) * dx,
 (x^2*z0^2) * dx,
 (x^2*z0^3) * dx,
 (x^2*z0^4) * dx,
 (x^3) * dx,
 (x^3*z0) * dx,
 (x^3*z0^2) * dx,
 (x^3*z0^3) * dx,
 (x^3*z0^4) * dx,
 (x^4) * dx,
 (x^4*z0) * dx,
 (x^4*z0^2) * dx,
 (x^4*z0^3) * dx,
 (x^4*z0^4) * dx,
 (x^5) * dx,
 (x^5*z0) * dx,
 (x^5*z0^2) * dx,
 (x^5*z0^3) * dx,
 (x^5*z0^4) * dx,
 (x^6) * dx,
 (x^6*z0) * dx,
 (x^6*z0^2) * dx,
 (x^6*z0^3) * dx,
 (x^6*z0^4) * dx,
 (x^7) * dx,
 (x^7*z0) * dx,
 (x^7*z0^2) * dx,
 (x^7*z0^3) * dx,
 (x^7*z0^4) * dx]
Increase precision.
[?7h[(x^2 - 2*x*z0 + z0^2) * dx,
 (2*x^3 + 2*x^2*z0 + z0^3) * dx,
 (-2*x^4 + x^3*z0 + z0^4) * dx,
 (x^3 - 2*x^2*z0 + x*z0^2) * dx,
 (2*x^4 + 2*x^3*z0 + x*z0^3) * dx,
 (-2*x^5 + x^4*z0 + x*z0^4) * dx,
 (x^4 - 2*x^3*z0 + x^2*z0^2) * dx,
 (2*x^5 + 2*x^4*z0 + x^2*z0^3) * dx,
 (-2*x^6 + x^5*z0 + x^2*z0^4) * dx,
 (x^5 - 2*x^4*z0 + x^3*z0^2) * dx,
 (2*x^6 + 2*x^5*z0 + x^3*z0^3) * dx,
 (-2*x^7 + x^6*z0 + x^3*z0^4) * dx,
 (x^6 - 2*x^5*z0 + x^4*z0^2) * dx,
 (2*x^7 + 2*x^6*z0 + x^4*z0^3) * dx,
 (2*x^7*z0 + 2*x^6*z0^2 + x^4*z0^4) * dx,
 (x^7 - 2*x^6*z0 + x^5*z0^2) * dx,
 (x^7*z0 - 2*x^6*z0^2 + x^5*z0^3) * dx,
 (x^7*z0^2 - 2*x^6*z0^3 + x^5*z0^4) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmatrix([[i - j for i in range(0, m)] for j in range(0, m)])[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef wyniki(n, infty_type):[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for d in range(1, 6):

....:     AS = as_cover(C, [C.x^d])

....:     AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAS1.holomorphic_differentials_basis()

 

 [?7h[?12l[?25h[?25l[?7lntials()[?7h[?12l[?25h[?25l[?7lrentials_basis()[?7h[?12l[?25h[?25l[?7lfor d in range(1, 6):

....:     AS = as_cover(C, [C.x^d])

....:     AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l

[][?7h[?12l[?25h[?25l[?7l[]

[?7h[?12l[?25h[?25l[?7l

 

 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: AS1

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
 z^5 - z = x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS1[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = 5[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: basis = AS1.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis = AS1.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: basis[0]

[?7h[?12l[?25h[?2004l[?7h(1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[0][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: basis[0].group_action([1])

[?7h[?12l[?25h[?2004l[?7h(1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[0].group_action([1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: basis[1]

[?7h[?12l[?25h[?2004l[?7h(z0) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[1][?7h[?12l[?25h[?25l[?7l[0].group_action([1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action([1])[?7h[?12l[?25h[?25l[?7l1].group_action([1])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: basis[1].group_action([1])

[?7h[?12l[?25h[?2004l[?7h(z0 + 1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis[1].group_action([1])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: basis[1].group_action([1]).coordinates()

[?7h[?12l[?25h[?2004l[?7h[1, 1, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 3[?7h[?12l[?25h[?25l[?7luo_rem(alpha*beta, t^4)[1][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l[?2004h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
[?2004l
[?2004h]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status
[?2004l
On branch master
Your branch is up to date with 'origin/master'.

Changes not staged for commit:
  (use "git add <file>..." to update what will be committed)
  (use "git restore <file>..." to discard changes in working directory)
	modified:   sage/.run.term-0.term
	modified:   sage/as_covers/as_cover_class.sage
	modified:   sage/as_covers/as_form_class.sage
	modified:   sage/as_covers/as_function_class.sage
	modified:   sage/as_covers/group_action_matrices.sage
	modified:   sage/drafty/draft.sage
	modified:   sage/init.sage

Untracked files:
  (use "git add <file>..." to include in what will be committed)
	.crystalline_p2.ipynb.sage-jupyter2
	.deRhamComputation.ipynb.sage-jupyter2
	.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
	.git.x11-0.term
	.superelliptic.ipynb.sage-jupyter2
	.superelliptic_alpha.ipynb.sage-jupyter2
	.superelliptic_arbitrary_field.ipynb.sage-jupyter2
	git.x11
	sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
	sage/drafty/2gpcovers.sage
	sage/drafty/as_cartier.sage
	sage/drafty/better_trace.sage
	sage/drafty/cartier_image_representation.sage
	sage/drafty/convert_superelliptic_into_AS.sage
	sage/drafty/draft4.sage
	sage/drafty/draft5.sage
	sage/drafty/draft6.sage
	sage/drafty/draft7.sage
	sage/drafty/draft8.sage
	sage/drafty/draft_klein_covers.sage
	sage/drafty/lift_to_de_rham.sage
	sage/drafty/pole_numbers.sage
	sage/superelliptic/frobenius_kernel.sage
	superelliptic_arbitrary_field.ipynb

no changes added to commit (use "git add" and/or "git commit -a")
[?2004h]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sage add git add C.x^33C.x^3C.x^33C.x^3 C.x^33C.x^3 sage/superelliptic/frobenius_kernel.sagesage/superelliptic/frobenius_kernel.sage
[?2004l
[?2004h]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u